Show that an ellipse has exactly 4 vertices, unless it is a circle.

Q: In an ellipse, the foci are at (-4, 3) and (4, 3) and one vertex is at (6, 3). How long is the major…

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Q: The vertices of the ellipse given by + =1 are 4

A: Given,           The equation of an ellipse is x24+y21=1To find: Vertices of the ellipse

Q: Find an equation of the ellipse that has center (-2, 3), a minor axis of length 10, and a vertex at…

A: Center=(h,k)=(-2,3) Length of minor axis= 2b=10 b=5    a= distance from center to vertex= distance…

Q: Give the property that defines all ellipses.

A: To determine: Properties that define all ellipses.

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

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Q: What is the general form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)7

A: Given query is to find the equation of the ellipse.

Q: Write the equation of the ellipse that is centered at (3, 3) and contains the following points:…

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Q: 3- Sketch the ellipse given that vertices at (8, 0), (-8, 0) and minor axis = 6.

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

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Q: 2. Explain how to identify the major and minor axes of an ellipse are by looking at both the graph…

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse b2

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Q: Find the equation of the ellipse with the given properties: Vertices at (± 7, 0) and endpoints of…

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Q: Find an equation of the ellipse that has center (-2, -3), a minor axis of length 10, and a vertex at…

A: Given x co-ordinate of centre and vertex are same , therefore type of ellipse is vertical. That is…

Q: State whether the given equation defines an ellipsoid or hyperboloid, and if a hyperboloid, whether…

A: Given, To determine whether the given equation defines an ellipsoid or hyperboloid, and if a…

Q: What are the general equations of an ellipse?

A: To write the general equation of an ellipse.

Q: Find the standard vertices of the ellipre X-

A: Here we have to find the standard equation of the hyperbola with the same vertices of the ellipse…

Q: What are the noteworthy distances of an ellipse?

A: Noteworthy distances of an ellipse

Q: The length of the major axis of an ellipse with foci at (-1, 2) and (3, 2) that passes through the…

A: Here we use basic defnition of major axis

Q: If the center of an ellipse is (3, –2), the major axis is horizontal and parallel to the x-axis, and…

A: An ellipse is a conic with eccentricity between 0 and 1. It has two axes: major axis and a minor…

Q: The line segment between the vertices of a hyperbola is called the _____ axis.

A: The difference in the distance between a point (x, y) and the two fixed points is a positive…

Q: If the major axis of an ellipse is 26 units in length and the minor axis is 10 units in length,…

A: Major axis of ellipse is a = 26 and minor axis is, b=10Therefore, the eccentricity of ellipse is…

Q: Give the geometric definition of a hyperbola.

A: Given: Give the geometric definition of a hyperbola.

Q: Find an equation of the ellipse that has center (-5, 5), a minor axis of length 6, and a vertex at…

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Q: how to determine the maximum and minimum distance of an ellipse given the major axis=477,736 and…

A: Length of the major axis is 477,736 Length of the minor axis is 477,078 We need to calculate the…

Q: All circles are ellipses, but not all ellipses are circles. A) True

A: Here use basic formula of ellipse and circle for comparing

Q: Find an equation of the ellipse that has center (1, -3), a minor axis of length 2, and a vertex at…

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Q: 4. The line segment with endpoints at the vertices of an ellipse is called the axis.

A: A conic section is obtained by the intersection of a plane with the surface of a cone. The three…

Q: How many distinguishable permutations are possible with all the letters of the word ELLIPSES?

A: The  complete solution is in given below

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: Find an equation of the ellipse that has center (-2, 5), a minor axis of length 8, and a vertex at…

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Q: What is the equation of the ellipse with center at (0, 0) and vertices at paints (2, 0). (0, 3), and…

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Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

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 equation of the ellipse with vertices at (−10, −4) and (6, −4), and covertices at (−2, −9)…

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Q: Write the equation of the ellipse that has a center at (2, – 4), a vertex at (7, – 4), and a…

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Q: The points where a hyperbola intersects the line through the foci are called the _____

A: The line through the foci is the major axis. Where it cuts the hyperbola is the vertices.Answer: The…

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: Find the standard form of the equation of ellipse satisfying the given conditions as Foci: (-2, 0),…

A: Given that the coordinates of foci of ellipse are (-2,0), (2,0)  and coordinates of vertices are…

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

A: Ellipse equation.

Q: An ellipse is a circle if and only if a-b equals what?

A: Given that an ellipse is a circle.

Q: Find the standard form of the equation of ellipse satisfying the given conditions as, end points of…

A: we have to find the standard form of the equation of the ellipse satisying the given conditions as…

Q: () and (.0) and 13. Vertices at one

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Q: Write the standard equation of an ellipse with center at (-2, 3), vertex at (-2,7) and a co-vertex…

A: Given data is: center -2,3, vertex -2,7, and co-vertex 1,3

Q: Draw the ellipse 5(? − 1) 2 + 4(? − 1) 2 = 25, labeling all important information.

A: Consider the ellipse  5x−12+4y−12=25

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.