What are the general equations of an ellipse?

Q: How is the equation of a hyperbola different from the equation of an ellipse?

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Q: Give the equation for the ellipse graphed

A: Center= (h,k)=(0,0) Length of the major axis=2a= 10 - (-10)=20  So, a=10 Length of the minor…

Q: Find an equation of the ellipse that has center (-3, 4), a minor axis of length 4, and a vertex at

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Q: Find an equation of the ellipse having a major axis of length 10 and foci at (-2, 4) and (-2, -2).

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Q: Find the equation of the ellipse in standard form and general form with foci (+4, 0) and major axis…

A: Find Equation of ellipse: Given, foci ±4,0 and Major axis of length 10.

Q: Given an equation of an ellipse in standard form, how do you determine whether the major axis is…

A: Standard form of ellipse:

Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (3,…

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Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A: Given : Endpoints of major axis: (1,8) and (1, -4) Endpoints of minor axis: (6,2) and (-4,2)

Q: What is an ellipse? What are the Cartesian equations for ellipses centered at the origin with foci…

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Q: Find the standard equation of the ellipse with center (5, 3), horizontal major axis of length 20,…

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Q: An ellipse has semi-major axis of 4 and its semi-minor axis is 3. The distance from the center of…

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Q: Find an equation in standard form for the ellipse graphed below.

A: the standard equation of the ellipse is given by as we can see here center of the ellipse is

Q: Find an equation of the ellipse with minor axis length 6, and vertices (3, 1) and (3,9).

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Q: State the equation of an ellipsoid?

A: An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.

Q: Find the standard form of the equation of the ellipse with the given characteristics. (5,6), (4,3),…

A: We are given the vertices as the following. (5,6), (4,3), (6,3), (5,0) Now, we have the following.

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A: Our Aim is to find the standrad form of the eliipse satisfying the given conditions:-Endpoints of…

Q: What is the equation of the standard ellipse with vertices at (±a, 0) and foci at (±c, 0)?

A: To find the equation of the standard ellipse with vertices ±a,0foci ±c,0

Q: What is the equation of this ellipse?

A: equation of ellipse with centre as origin and a and b are semi major and minor axis. here a = 1 b =…

Q: Find an equation for the ellipse with center (2, 0), foci (2, ±3) and major axis of length 8.

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Q: What is the minor radius of this ellipse?

A: Query- What is the minor radius of this ellipse. Answer- An ellipse is a plane curve surrounding two…

Q: Find an equation of the ellipse having a major axis of length 6 and foci at (−5, −1) and (−5, −5).

A: Here the y coordinate of the focus is Changing so we can say that major axis of the ellipse is…

Q: What are the noteworthy distances of an ellipse?

A: Noteworthy distances of an ellipse

Q: What is the equation of the given ellipse? YA

A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

Q: what are the turning point? what is the number of turning points in an ellipse?

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Q: Explain with the help of an example Parametrization of an Ellipse.

A: We have write the parametrization of an ellipse.

Q: Find the standard form of the equation of the ellipse.  Vertices: (3,1) and (3,7) Eccentricity:…

A: The standard equation of the vertical ellipse having centre at (h,k) and eccentricity…

Q: Find the standard form of the equation of the ellipse with the given characteristics. Center (3,-5)…

A: Center of the ellipse is h, k=3, -5, a=3c and foci are 3, -6 & 3, -4. Now c is the distance…

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A: Here first we will find center point of ellipse then we will find values of a2 and b2 , then we will…

Q: Obtain the Cartesian equation of the ellipse using its definition.

A: Let us take the following ellipse into consideration with center at the origin (0,0) and foci as…

Q: 11. Explain how to identify the major and minor axes of an ellipse are by looking at both the graph…

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Q: d an equation of the ellipse that has center (1, 3), a major axis of length 6, and endpoint of minor…

A: Given, The center of the ellipse =1,3 Length of the major axis = 6 End point of the minor axis = 1,…

Q: Construct an ellipse having length of major axes and minor axes equal to 12 cm and 9 cm…

A: Given: major axes=2a=12  cmminor axes=2b=9  cm

Q: The line segment perpendicular to the major axis, with endpoints on the ellipse, and passing through…

A: To find the axis where the line segment perpendicular to the major axis, with endpoints on the…

Q: find the standard equation of an ellipse centered at the origin whose major axis is horizontal and…

A: We know that standard equation of an ellipse centered at the (h,k) whose major axis is horizontal…

Q: Find an equation in standard form of the ellipse described. Center (3, 4); passes through (3, 8)…

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Q: What features are unique to an ellipse?

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Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (3,…

A: Under this case, vertices are given by (xc, yc ± a)

Q: What is the general form of equation of an ellipse if its center is at (3,-1), a = 4, b = 3 and its…

A: The general form is,                            (x-c)2/a2 + (y-d)2/b2  =1. Where (c,d) is centre of…

Q: What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and…

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Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (3,…

A: Ellipse equation.

Q: the equation of this ellipse

A: Here we have to find the equation of the ellipse,  we have;

Q: Find an equation of the ellipse that has center (0, 3),

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Q: Why should we transform a given equation of an ellipse into its standard form

A: Given, Why should we transform a given equation of an ellipse into its standard form ?

Q: Write an equation for the ellipse

A: In this question we have to write an equation for the ellipse.

Q: The line segment with endpoints at the vertices of an ellipse is called the _____ axis.

A: The line segment with endpoints at the vertices of an ellipse is called the _____ axis.

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.