What is an ellipse? What are the Cartesian equations for ellipses centered at the origin with foci on one of the coordinate axes?How can you find the foci, vertices, and directrices of such an el-lipse from its equation?

Q: Find the standard form of the equation of the ellipse satisfying the following conditions. Major…

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Q: 4. Determine the equation of an ellipse having foci (0,+V5) and vertices (0, +4).

A: topic - equation of ellipse

Q: Find the standard form of the equation of an ellipse with the given characteristics. Foci (0,-1) and…

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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: Choose one: If the foci of an ellipse are close to the center of the ellipse, then the graph will…

A: If the foci of an ellipse are close to the center of the ellipse, then the graph will appeaer.a.…

Q: 13.) Find an equation for the ellipse that satisfies: 1 ессentricity and foci(0,±2) 3

A: Given: The eccentricity =13 and foci 0,±2 of an ellipse To find: The equation of the ellipse.

Q: 4. Determine the equation of an ellipse having foci (0, ±9) and major axis length 22.

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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: If the foci of an ellipse are(-4,4) and(6,4) , then the coordinates of the center of the ellipse…

A: Given : The statement , If the foci of an ellipse are(-4,4) and(6,4) , then the coordinates of the…

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 with the given characteristics. Vertices: (0,…

A: Now center of the ellipse is the midpoint of the line segment joining the vertices. That is, Now…

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

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Q: ind an equation in standard form for the ellipse with center at (8, 6), horizontal major axis of…

A: Given: center =(8,6) horizontal major axes of the length =6 Passing through the point =(9,5)

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 the equation in standard form for an ellipse that has foci at (1,2) and (-3,2) and a vertex at…

A: The standard form of the equation of an ellipse with center  ( h ,   k )  and major axis parallel to…

Q: An ellipse has a semi-major axis of 5cm and an eccentricty of 0.4. What is the maximum length of the…

A: Maximum length of ellipse = length of major axis = 2×(length of semi major axis)

Q: Find an equation for the ellipse that satisfies the given conditions. Length of major axis: 6,…

A: Given,Length of major axis = 6           length of minor axis = 4  and  foci on x-axis

Q: Find an equation for the ellipse that satisfies the given conditions. Endpoints of minor axis: (0,…

A: Given  End points of minor axis  : (0,±3)  Distance between foci: 8

Q: Find an equation for the ellipse with Center at: (0, 0) Foci at: (+5, 0) Vertices at: (±6, 0)

A: 6. The ellipse have center at 0,0 , foci ±5,0 and vertices ±6,0  Note: Multiple questions are given,…

Q: 5. The line segment perpendicular to the major axis, with endpoints on the ellipse, and passing…

A: Fill the blank

Q: Find the standard form of the equation of the ellipse with the given characteristics. Center: (2,…

A: Given ellipse with:

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

A: Given:- Center: (3,-4); vertex(3, -5/2) minor axis of length 2 To find:- standard equation of…

Q: 7. FIND THE EQUATION OF THE ELLIPSE WITH FOCI: (-4,0) AND MAJOR AYIS LENGTH = 6 (も)

A: Given:    Foci : -4,0,(-4,4) or ±4,0   Major axis length = 6  Here the foci is are on x-axis ,so…

Q: 4. Consider the ellipse which has its center at (-1, 5), a vertex at (-1, 0), and a covertex at (-5,…

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Q: Find an equation for the ellipse that satisfies the given conditions. Endpoints of major axis: (410,…

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Q: An ellipse has foci at (1, 5) and (1, −1), and it goes through the points (−1, 2) and (3, 2). Sketch…

A: Given data is: An ellipse has foci at (1, 5) and (1, −1), and it goes through the points (−1, 2) and…

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

A: we have to find the standard form of the equation of the ellipse with the given characteristics.…

Q: What is the standard form equation of the ellipse that has vertices (±8, 0) and foci (±5, 0)? Sketch…

A: Standard form of equation of ellipse is

Q: What is a hyperbola? What are the Cartesian equations for hyperbolas centered at the origin with…

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Q: Find an equation for the ellipse that satisfies the given conditions. Length of major axis: 6,…

A: Since foci is on y axis therefore it is a vertical ellipse.

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

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Q: 4. Find an equation for the ellipse with Center at: (0, 0) Focus at: (2, 0) Vertex at: (5, 0)

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Q: Find the standard form of the equation for the ellipse centered at (0,0), having vertical major axis…

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Q: 2. Identify the coordinates of the foci, vertices and covertices of the ellipse x2 y2 with equation…

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Q: Q2- Explain how to find the center, foci, vertices and co-vertices of an ellipse if you are given…

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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: 1) WHAT IS THE DIFFERENCE BETWEEN THE EQUATIONS FOR PARABÓLAS, ELLIPSES, CIRCLES AND HYPERBOLAS?

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Q: the earth revolves around the sun along an ellipse. the sun lies in the focus of the ellipse. The…

A: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse. The…

Q: Find an equation of the ellipse with the given characteristics. Vertices: (0, ±3); eccentricity:  1…

A: Given, Vertices: (0, ±3),  eccentricity : e=12

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 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 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: Ellipses centered at the origin have symmetry with respect to the x-axis, y-axis, and the origin.…

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Q: Determine the eccentricity of an ellipse whose foci and directrices are 4 units and 9 units apart,…

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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.