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Ellips axis

Each axis is the perpendicular bisector of the other. That is, each axis cuts the other into two equal parts, and each axis crosses the other at right angles. The focus points always lie on the major (longest) axis, spaced equally each side of the center. See Foci (focus points) of an ellipse The major axis of ellipse lies along x-axis and is the longest width across it. It has length equal to 2a. The endpoints are the vertices of major axis, having coordinates (h±a,k). Minor axis lies along y-axis and is smallest width across it. It has length equal to 2b. The endpoints are the vertices of minor axis having coordinates (h, k±b) Every ellipse has two axes of symmetry. The longer axis is called the major axis, and the shorter axis is called the minor axis.Each endpoint of the major axis is the vertex of the ellipse (plural: vertices), and each endpoint of the minor axis is a co-vertex of the ellipse. The center of an ellipse is the midpoint of both the major and minor axes. The axes are perpendicular at the center That is, the axes will either lie on or be parallel to the x- and y-axes. Later in the chapter, we will see ellipses that are rotated in the coordinate plane. To work with horizontal and vertical ellipses in the coordinate plane, we consider two cases: those that are centered at the origin and those that are centered at a point other than the origin

Major / minor axis of an ellipse - Math Open Referenc

Free Ellipse calculator - Calculate ellipse area, center, radius, foci, vertice and eccentricity step-by-ste Ellips kan syfta på: . Ellips (matematik) - en geometrisk figur i ett plan, en geometrisk ort för en punkt Ellips (litteratur) - en ellips som en utelämning av en viss tidsperiod i en berättelse Ellips (retorik) - en retorisk stilfigur och tankefigur i uttryck som kännetecknas av att en del av satsen utelämnas Ellips (syntax) - ett visst ord eller ibland flera ord utelämnas. The major axis is the segment that contains both foci and has its endpoints on the ellipse. These endpoints are called the vertices. The midpoint of the major axis is the center of the ellipse.. The minor axis is perpendicular to the major axis at the center, and the endpoints of the minor axis are called co-vertices.. The vertices are at the intersection of the major axis and the ellipse

Ellipse (Definition, Equation, Properties, Eccentricity

Be careful: a and b are from the center outwards (not all the way across). (Note: for a circle, a and b are equal to the radius, and you get π × r × r = π r 2, which is right!) Perimeter Approximation. Rather strangely, the perimeter of an ellipse is very difficult to calculate, so I created a special page for the subject: read Perimeter of an Ellipse for more details I want to plot an Ellipse. I have the verticles for the major axis: d1(0,0.8736) d2(85.8024,1.2157) (The coordinates are taken from another part of code so the ellipse must be on the first quadrant of the x-y axis) I also want to be able to change the eccentricity of the ellipse Ellipse, a closed curve, the intersection of a right circular cone (see cone) and a plane that is not parallel to the base, the axis, or an element of the cone. It may be defined as the path of a point moving in a plane so that the ratio of its distances from a fixed point (the focus) and a fixe Ex 11.3, 20 Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2). Since Major axis is on the x-axis So required equation of ellipse is ^/^ + ^/^ = 1 Given that ellipse passes through poin

Equations of Ellipses College Algebr

Rotating Points First, we will rotate a point (x1, y 1) around the origin by an angle a. 5 10 15 20 25 30 35 40 45 50 55 5 10 15 20 25 30 35 40 45 50 55 b a a+b r r (x,y) x y (x 1 , y 1 ) x 1 y 1 If the point (x1, y 1) is at angle b from the x-axis, then Axis Endpoint. Defines the first axis by its two endpoints. The angle of the first axis determines the angle of the ellipse. The first axis can define either the major or the minor axis of the ellipse. Distance to Other Axis Defines the second axis using the distance from the midpoint of the first axis to the endpoint of the second axis (3) Let these axes be AB and CD. With a radius equal to half the major axis AB, draw an arc from centre C to intersect AB at points F1 and F2. These two points are the foci. For any ellipse, the sum of the distances PF1 and PF2 is a constant, where P is any point on the ellipse. The sum of the distances is equal to the length of the major axis Length of the semi-major axis = (AF + AG) / 2, where F and G are the foci of the ellipse, and A is any point on the ellipse.That's pretty easy! Let's try putting this formula into action. Example.

What is Ellipse? The Ellipse in mathematics is a curve in a place surrounded by two focal points where the sum of distances between two focal points is always constant. Ellipse is the generalization of a circle or we can call it as the special type of Ellipse containing two focal points at similar locations Parameters: xy (float, float). xy coordinates of ellipse centre. width float. Total length (diameter) of horizontal axis. height float. Total length (diameter) of vertical axis. angle float, default: 0. Rotation in degrees anti-clockwise Typically, an axis passes all the way through an object and is an axis of symmetry. In the semi case that is not so. Also, they are usually used as a length (see Area of an ellipse) rather than a line segment. For these reasons, some prefer to call them the major radius and minor radius of the ellipse. Other. axis are perpendicular to the plane of the ellipse. The white plastic rod depicts the imaginary axis and represents the minor axis orientation. In order to prove this point, make an enlarged photo copy of this page: set the photo copier enlargement for 150 percent

The Ellipse - Algebra and Trigonometr

Jan 24, 2017 · We can start from the parametric equation of an ellipse (the following one is from wikipedia), we need 5 parameters: the center (xc, yc) or (h,k) in another notation, axis lengths a, b and the angle between x axis and the major axis phi or tau in another notation.. xc <- 1 # center x_c or h yc <- 2 # y_c or k a <- 5 # major axis length b <- 2 # minor axis length phi <- pi/3 # angle of major. Ellipse miniature inertial navigation sensors show amazing performance for its small size. Motion, meter or centimeter level navigation, check out all model The ellipse belongs to the family of circles with both the focal points at the same location. In an ellipse, if you make the minor and major axis of the same length with both foci F1 and F2 at the center, then it results in a circle. Area of an Ellipse. Area= π ab. Where a and b denote the semi-major and semi-minor axes respectively

Axes of ellipse. А 1 А 2 = 2 a - major axis (larger direct that crosses focal points F 1 and F 2). B 1 B 2 = 2 b - minor axis (smaller direct that perpendicular to major axis and intersect it at the center of the ellipse О). a - semi-major axis. b - semi-minor axis. O - center of the ellips The major axis of the ellipse is the longest width across it. For a horizontal ellipse, that axis is parallel to the [latex]x[/latex]-axis. The major axis has length [latex]2a[/latex]. Its endpoints are the major axis vertices, with coordinates [latex](h \pm a, k)[/latex]. Minor Axis. The minor axis of the ellipse is the shortest width across it You can call this the semi-major axis instead. 2. Find the minor radius. As you might have guessed, the minor radius measures the distance from the center to the closest point on the edge. Call this measurement b. This is at a 90º right angle to the major Nederlands: De oppervlakte van een ellips berekenen

Oval. An oval (from Latin ovum, egg) is a closed curve in a plane which loosely resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry In Fig. 4, 5, & 6 we have rotated the major axis by 20 degrees (clockwise) and we have changed the ratio between the major and minor axis. The left ellipse (fatter ellipse) now has a 40 degree (1:1.55) width to height ratio and the right ellipse (skinnier ellipse) has a 20 degree (1:2.92) ratio In our case, the largest variance is in the direction of the X-axis, whereas the smallest variance lies in the direction of the Y-axis. In general, the equation of an axis-aligned ellipse with a major axis of length and a minor axis of length , centered at the origin, is defined by the following equation: (1

Off-axis Mirrors - Interspectrum

Ex 8.1, 4 Find the area of the region bounded by the ellipse ﷮2﷯﷮16﷯+ ﷮2﷯﷮9﷯=1 Equation Of Given Ellipse is :- ﷮2﷯﷮16﷯+ ﷮2. How to get the radius of an ellipse at a specific angle by knowing its semi-major and semi-minor axes? Please take a look at this picture The minor axis length is given by 2 b = 4 d) Locate the x and y intercepts, find extra points if needed and sketch. Matched Problem: Given the following equation 4x 2 + 9y 2 = 36 a) Find the x and y intercepts of the graph of the equation. b) Find the coordinates of the foci. c) Find the length of the major and minor axes Sorry if this is a stupid question, but is there an easy way to plot an ellipse with matplotlib.pyplot in Python? I was hoping there would be something similar to matplotlib.pyplot.arrow, but I can't find anything.. Is the only way to do it using matplotlib.patches with draw_artist or something similar? I would hope that there is a simpler method, but the documentation doesn't offer much help

As stated, using the definition for center of an ellipse as the intersection of its axes of symmetry, your equation for an ellipse is centered at $(h,k)$, but it is not rotated, i.e. the axes of symmetry are parallel to the x and y axes Calculates the area, circumference, ellipticity and linear eccentricity of an ellipse given the semimajor and semininor axes el·lipse (ĭ-lĭps′) n. 1. A plane curve, especially: a. A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone. b. The locus of points for which the sum of the distances from each point to two fixed points is equal. 2. Ellipsis. [French, from Latin ellīpsis, from Greek elleipsis, a falling short. Equation of an Ellipse. An ellipse is a conic section, formed by the intersection of a plane with a right circular cone.The standard form for the equation of the ellipse is: $\displaystyle{\frac{\left(x-h\right)^2}{a^2} + \frac{\left(y-k\right)^2}{b^2} = 1}

Lesson EQUATION OF AN ELLIPSE

If the center of the ellipse is moved by x = h and y = k then the equations of the ellips become: Find the equation of the ellipse that has accentricity of 0.75, and the foci along 1. x axis 2. y axis, ellipse center is at the origin, and passing through the point (6 , 4) Assuming that the axes have not been rotated: In the standard form equation, look at the numbers in the denominators. They are the squares of half the lengths of the axes of the ellipse parallel to the respective variable. If the number under the fraction involving (x-h)^2 is larger than the number under the other fraction, then the major axis of the ellipse is parallel to the x-axis of the. Figure 4-45.-Ellipse by four-center method. ELLIPSE BY FOUR-CENTER METHOD The four-center method is used for small ellipses. Given major axis, AB, and minor axis, CD, mutually perpendicular at their midpoint, O, as shown in figure 4-45, draw AD, connecting the end points of the two axes. With the dividers set to DO, measure DO along AO and reset the dividers on the remaining distance to O where a and b are mentioned as in the preceding bullets, and F is the distance from the center to each focus.. This figure shows a horizontal ellipse and a vertical ellipse with their parts labeled. Notice that the length of the major axis is 2a, and the length of the minor axis is 2b.This figure also shows the correct placement of the foci — always on the major axis It is also equal to the distance between the two foci and the semi-major axis: e = PF/PD = f/a. When the semi-major axis and the semi-minor axis coincide with the Cartesian axes, the general equation of the ellipse is given as follows. x 2 /a 2 + y 2 /b 2 = 1. The geometry of the ellipse has many applications, especially in physics

The major axis is on the y -axis. The x -intercepts are ( ± b , 0 ) and the y -intercepts are ( 0 , ± a ) . Notice that the major axis is horizontal if the x 2 -term has the larger denominator and vertical if the y 2 -term has the larger denominator Where: a = semi-major axis length of an ellipse b = semi-minor axis length of an ellipse π = 3.14159265

ellipse has two vertices. The axis AA ′ is called major axis. The length of the major axis is AA ′ = 2a iv) Put x = 0 ⇒ y2 = b 2 ⇒ y = ± b. Thus, the curve meets y-axis (another axis) at two points B(0, b), B ′(0, -b). The axis BB ′ is called minor axis and the length of the minor axis is BB ′ = 2b The major axis is the x axis and its length is equal to 2a = 6/5 = 1.2 Solution to Problem 2 a) Divide all terms of the equation by 32 to obtain x 2 / 4 + y 2 / 16 = 1 The above equation may be written as follows x 2 / b 2 + y 2 / a 2 = 1 with a = 4 and b = 2 and a > b. Hence the major axis is the y axis and the minor axis is the x axis Line CD is the Minor Axis and is the perpendicular bisector of the Major Axis. Lines OC and OD are the Semi-Minor axes which also equals Line b. Points f 1 and f 2 are the foci of the ellipse. Points A and B are called apses. Johannes Kepler's First Law states that the planets move in elliptical orbits with the Sun located at one of the foci The ellipse's minor-axis radius. Must be non-negative. rotation The rotation of the ellipse, expressed in radians. startAngle The angle at which the ellipse starts, measured clockwise from the positive x-axis and expressed in radians. endAngle The angle at which the ellipse ends, measured clockwise from the positive x-axis and expressed in radians Total length (diameter) of horizontal axis. height: float. Total length (diameter) of vertical axis. angle: scalar, optional. Rotation in degrees anti-clockwise. Notes. Valid keyword arguments are. Property Description; agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array

Find the length of the major or minor axes of an ellips

  1. Specify axis endpoint of ellipse or [ Arc/ Center/ Isocircle]: Geef een punt op of voer een optie in Axis Endpoint Hiermee definieert u de eerste as aan de hand van de twee eindpunten. De hoek van de eerste as bepaalt de hoek van de ellips. De eerste as kan zowel de primaire als de secundaire as van de ellips zijn. Distance to Other Axis
  2. ator of x is greater, so t he ellipse is symmetric about x-axis. Center : In the above equation no number is added or subtracted with x and y. So the center of the ellipse is C (0, 0) Vertices : a ² = 25 and b ² = 9 a = 5 and b = 3. Vertices are A(a, 0) and A'(-a, 0
  3. or axis c, A the moment of inertia about the

Ellips (matematik) - Wikipedi

How to Hand Draw an Ellipse. Drawing an ellipse is often thought of as just drawing a major and minor axis and then winging the 4 curves. This is good enough for rough drawings; however, this process can be more finely tuned by using.. General Equation of an Ellipse. The standard equation for an ellipse, x 2 / a 2 + y 2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes

Quadratic surfaces of revolutionConstruction of Ellipse by Describing Circles | ClipArt ETC

Ellipsoid - Wikipedi

x-axis distance from the polar axis y-axis axis of rotation, z-axis IV. Important Notes A. Equations Valid Only on Ellipse The equations that follow are valid only on an ellipse. They are not valid off the ellipse. In geodesy any point not on the ellipsoid is not on the ellipse as far as these equations are concerned Ellipse 1. Analytical Geometry Ellipse T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com 2. Ellipse An ellipse is the set of all points in a plane such that the sum of the distances from two points (foci) is a constant. When you go from point F to any point on the ellipse and hen go on to point G, you will always trav ellipse definition: 1. a regular oval shape 2. a regular oval shape 3. a curve in the shape of an oval. Learn more Ellipse definition, a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal. It is a conic section formed by the intersection of a right circular cone by a plane that cuts the axis and the surface of the cone. Typical equation: (x2/a2) + (y2/b2) = 1. If a = b the ellipse is a circle Above equations are valid when axes are x and y-axis. In the case of axes different from x and y-axis, the equation will be,and L 1 = 0 and L 2 = 0 are the major and minor axis. 2.2 Terminology of the ellipse (when axes are x and y-axis) (a) The line joining two focuses (F 1 and F 2) are called as the focal axis or major axis

Ellipse definition is - oval. The property of an ellipse. b: a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant : a plane section of a right circular cone that is a closed curv An ellipse is the set of all points, the sum of whose distances from two fixed points is a given positive constant that is greater than the distance between the fixed points. The two fixed points ar

Ellips översättning i ordboken svenska - engelska vid Glosbe, online-lexikon, gratis. Bläddra milions ord och fraser på alla språk Ellipser er en av den type figurer som går under fellesbetegnelsen kjeglesnitt (sammen med sirkel, parabel og (link) hyperbel). De kalles kjeglesnitt fordi de fremkommer hvis man skjærer en kjegle over et bestemt plan. Brennpunkt

(The major axis is the maximum length from the one end to the other.) However if we have a sphere and squash it to make a shorter fatter shape (a bit like a burger). In such case it is called an oblate ellipsoid. If we chop it through the middle to get a circle, then the volume is the area of the circle times 2/3rd of the minor axis How to plot contours only inside ellips?. Learn more about contour, plo This is the y-axis. And we immediately see, what's the center of this? The center is going to be at the point 1, negative 2. And if that's confusing, you might want to review some of the previous videos. Center's at 1, x is equal to 1. y is equal to minus 2. That's the center. And then, the major axis is the x-axis, because this is larger An ellipse has a major and a minor axis. Also we want to be able to plot the ellipse on different center points. Therefore we write a function whose inputs and outputs are: Inputs: r1,r2: major and minor axis respectively C: center of the ellipse (cx,cy) Output: [x,y]: points on the circumference of the ellips Sumbu utama atau transvers axis adalah sumbu simetri kurva elips yang melaui titik folus $ F_1 $ dan $ F_2 $, ditunjukkan oleh sumbu X. *). Sumbu sekawan atau cojugate axis adalah sumbu simetri kurva elips yang melaui titik pusat dan tegak lurus dengan sumbu utama, ditunjukkan oleh sumbu Y. *). Titik puncak elips

ellips- översättning i ordboken svenska - engelska vid Glosbe, online-lexikon, gratis. Bläddra milions ord och fraser på alla språk An ellips is a curve with equation x²/a² + y²/b² = 1 In this equation a is the semi major axis, b the semi minor axis. Drag the green points on the horizontal and the vertical axis and see how the equation and the form of the ellips change The longer axis is called the major axis, and the shorter axis is called the minor axis. Each endpoint of the major axis is the vertex of the ellipse (plural: vertices), and each endpoint of the minor axis is a co-vertex of the ellipse. The center of an ellipse is the midpoint of both the major and minor axes. The axes are perpendicular at the. That is the major axis of the ellipse. If a is larger than b, the major axis lies along the x-axis, and we leave it to you to show that in such a case. R 1 + R 2 = 2a [Hint: Make a sketch of the ellipse and the axes which define it, mark one of the points at which it crosses the x-axis, and examine R 1 and R 2 of that point]

Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose endpoints lie on the ellipse as shown below. Let's find the length of the latus rectum of the ellipse x 2 /a 2 + y 2 /b 2 = 1 shown above. Let the length of AF 2 be l. Therefore, the coordinates of A are (c, l) ELLIPS. ELLIPS h, r. Half ellipsoid. Its cross-section in the x-y plane is a circle with a radius of r centered at the origin. The length of the half axis along the z-axis is h. Example: ELLIPS r, r ! hemisphere.. A vertical major axis means the ellipse will have greater height than width. If the major axis is vertical, then the formula becomes: `x^2/b^2+y^2/a^2=1` We always choose our a and b such that a > b. The major axis is always associated with a. Example 2 - Ellipse with Vertical Major Axis . Find the coordinates of the vertices and foci o

Since the ellipse minor axis always goes through the center of our square this is something we can use to help us draw it. Conversely the major axis references nothing that can help us in locating it in our perspective square. This is why I do not recommend using the major axis when drawing ellipses These axes might be thought of as corresponding to two diameters of a circle, but in a circle ALL the diameters are the same length. The 'centre' of an ellipse is the point where the two axes cross. But, more important are the two points which lie on the major axis, and at equal distances from the centre, known as the foci (pronounced 'foe-sigh') The Principal Axes Theorem: Let Abe an n x n symmetric matrix. Then there is an orthogonal change of variable, x=P y, that transforms the quadratic form xT A x into a quadratic from yT D y with no cross-product term (x 1x2) (Lay, 453). Example: Ellipse Rotation Use the Principal Axes Theorem to write the ellipse in the quadratic form with no.

Ellipse Calculator - eMathHel

  1. SVG Ellipse - <ellipse> The <ellipse> element is used to create an ellipse. An ellipse is closely related to a circle. The difference is that an ellipse has an x and a y radius that differs from each other, while a circle has equal x and y radius
  2. or axis and perpendicular to the major axis. In the picture to the right, the distance from the center of the ellipse (denoted as O or Focus F; the entire vertical pole is known as Pole O) to directrix D is p. Directrices may be used to find the eccentricity of an ellipse
  3. or axis goes through the shorter distance. The major axis is always associated with the variable a and equals 2a. (a is the distance from the center point to the ellipse along the major axis, so you have to double that to get the length of the entire axis.) The

Synonymer till ellips - Synonymer

Note: If b > a, then the focal axis will be parallel to the y-axis. This will be obvious when you sketch the ellipse, and the associated Pythagorean relation will be c2 = b2 a2 (you want c to be a real number, so that is what guides your choice of using c 2= a2 b (focal axis parallel to x-axis) or c2 = b2 a2 (focal axis parallel to y-axis) Given an ellipse with a semi-major axis of length a and semi-minor axis of length b.The task is to find the area of an ellipse. In mathematics, an ellipse is a curve in a plane surrounding by two focal points such that the sum of the distances to the two focal points is constant for every point on the curve or we can say that it is a generalization of the circle

Ellips - Grade fruit and vegetables more accurately than

  1. Creates an ellipse with two focal points and semimajor axis length. Example: Ellipse((0, 1), (1, 1), 1) yields 12x² + 16y² - 12x - 32y = -7 . Note: If the condition: 2*semimajor axis length > Distance between the focus points isn't met, you will get an hyperbola
  2. Now, this tells you where the foci are--they both lie on the major axis, at a distance of c from the center of the ellipse. But if you are trying to calculate the radius of curvature at the point y end (where the major axis intersects the ellipse), you can work directly from the formula for the ellipse
  3. or axis makes it oblate. A more general figure has three orthogonal axes of different lengths a, b and c, and can be represented by the equation x 2 /a 2 + y 2 /b 2 + z 2.
  4. or axis of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle

How to Find the Major Axis of an Ellipse - Video & Lesson

  1. or axis, (h, k) are the coordinates of the cente
  2. dre principalaxeln (
  3. Conics as cross sections of a circular cone.Conics are given by the intersection of a plane with a circular cone. The intersection will correspond to one of the conic curves (ellipse, hyperbola, parabola, etc.) depending on the angle at which the plane cuts the cone
  4. or axis is half of the

Ellipse Calculator - Symbola

Your radius in your x-direction is 3. 3 squared is equal to 9. So your x-radius is actually larger than your y-radius. So, it's going to be a little bit of a fat ellipse. Actually, let me draw the axes first. Let me draw it like this. That's my vertical axis, this is my x-axis. And so my center is now at minus 2, 1. That's minus 2, and I go up one 3.5 Parabolas, Ellipses, and Hyperbolas A parabola has another important point-the focus. Its distance from the vertex is called p. The special parabola y = x2 has p = 114, and other parabolas Y = ax2 have p = 1/4a.You magnify by a factor a to get y = x2.The beautiful property of

2 Ellipses With Equal Vertical Axes | ClipArt ETCKepler and ellipsesWriting Equations of Ellipses in Standard Form

Ellips-Hiperbola - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. fisma An ellipse equation, in conics form, is always =1.Note that, in both equations above, the h always stayed with the x and the k always stayed with the y.The only thing that changed between the two equations was the placement of the a 2 and the b 2.The a 2 always goes with the variable whose axis parallels the wider direction of the ellipse; the b 2 always goes with the variable whose axis. Ellipse smart bike lock sends you an alert if your bike is disturbed. 17mm thick forged steel with dual locking & bank-level encryption prevent theft Determine the equation of the ellipse that is centered at (0, 0), passes through the point (2, 1) and whose minor axis is 4. Exercise 5. The focal length of an ellipse is 4 and the distance from a point on the ellipse is 2 and 6 units from each foci respectively. Calculate the equation of the ellipse if it is centered at (0, 0). Exercise The major axis is \(2a=4\), and the minor axis is \(2b=2\). Writing Equations of Ellipses. You may be asked to write an equation from either a graph or a description of an ellipse: Problem. Write the equation of the ellipse: Solution An approximation for the average/mean radius of an ellipse's circumference, , is the elliptical quadratic mean: (where is the central, horizontal, transverse radius/semi-major axis and is the central, vertical, conjugate radius/semi-minor axis) As a meridian of an ellipsoid is an ellipse with the same circumference for a given set of values, its average/mean radius, , is also the same as for.

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