Express the equation of an ellipse 5x' +4y-40x+8y+64 =0 in standard form. Hence, sketch the ellipse.

Q: Find an equation of the ellipse that has center (0, 5), a major axis of length 4, and endpoint of…

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

A: Origin is centre (h,k) = (0,0) Major axis is horizontal axis. length of major axis = a = 10 length…

Q: Find an equation of the ellipse having a major axis of length 8 and foci at (1, 5) and (-3, 5). O=0

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Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

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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 an equation of the ellipse that has center (-3, 4), a major axis of length 12, and endpoint of…

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Q: Find an equation of the ellipse with minor axis of length 8 and vertices at (-9, 3) and (7, 3).

A: The solution is given in the next step.

Q: Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3) and (-5, -1).…

A: Given problem:- Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3)…

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

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Q: Find the standard form of the equation of an ellipse with the given characteristics. Vertices…

A: Given Vertices (-a,0)=(-11,0) and (-a,0)= (11,0) ⇒a=11 Endpoints of minor axis (0,-b)= (0,-6) and…

Q: Find the standard form of the equation of ellipse satisfying the given conditions as  Major axis…

A: It is given that an ellipse whose major axis is horizontal with length 8, length of minor axis is…

Q: Find the points on the ellipse  5x2 + y2 = 5  that are farthest away from the point (1, 0).

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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 are the general equations of an ellipse?

A: To write the general equation of an ellipse.

Q: Center at (-2,3): major axis is horizontal; passing through (1,4) and (2,3)

A: The center at (-2,3), the major axis is horizontal and passing through (1,4) and (2,3). We have to…

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: Find an equation of the ellipse that has center (3, -4), a major axis of length 4, and endpoint of…

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Q: What is the equation of an ellipse having vertices at and a minor axis (0,+8,) which is 6 units in…

A: the standard equation of the vertical ellipse is given by x-h2a2+y-k2b2=1

Q: Find the center, length of major and minor axis for ellipse 4x +9y + 24x = 0 Hence, sketch the…

A: Solutions

Q: Find the standard equation of the ellipse whose major and minor axes are the transverse and…

A: We need to find standard equation of ellipse.

Q: Find the equation of the ellipse whose centre is at thte origin, foci are (1,0) and (-1,0) and…

A: Here we have to find the equation of the ellipse whose center is at origin, foci are 1,0 and -1,0…

Q: Write the standard form equation of the ellipse. Major axis vertical with length 16. Minor axis…

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Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

A: Given that: Centre of ellipse =(4, -4)Major axis, 2a=8End point of minor axis = (7, -4)

Q: Which of the following is the equation of a vertical ellipse with center (4,6) Major axis s = 18 and…

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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: What is the standard form equation of an ellipse with the center (-1, 6), a horizontal major axis…

A: Center (h,k) = (-1,6) a = 22 b = 8

Q: Find an equation of the ellipse that has center (-5, 4), a major axis of length 6, and endpoint of…

A: Length of major axis of an ellipse is 2a

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

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Q: Find an equation of the ellipse that has center (-3, 0), a minor axis of length 4, and a vertex at…

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Q: Find the points on the ellipse 4x2 + y2  = 4 that are farthestaway from the point  (1,0 ).

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Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

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Q: Find an equation of the ellipse having a major axis of length 12 and foci at (2, 3) and (-6, 3).

A: Let us find the equation of ellipse when major axis & foci are given.

Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

A: We need to find equation of ellipse.

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (х, у) %3…

A: The distance between of two-points: - The length of the line segment connecting two places is the…

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

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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: What is the equation of a vertical ellipse with a center at point (8,-4), a major axis that is 12…

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Q: Find an equation of the ellipse that has center (-5, 3), a major axis of length 10, and endpoint of…

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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: Find an equation of the ellipse having a major axis of length 12 and foci at (6, –3) and (-4, –3).…

A: Explanation and solutions is given below....

Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: Find the standard form of the equation of an ellipse with the given characteristics. Major axis…

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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 an ellipse with the given characteristics. Major axis…

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

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Q: Find an equation of the ellipse that has center (-3, 5), a minor axis of length 2, and a vertex at…

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Q: Find an equation of the ellipse having a major axis of length 8 and foci at (5, -3) and (-1, -3).…

A: Finding the equation of ellipse

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: Find the standard form of the equation of ellipse satisfying the given conditions as  Major axis…

A: Given- An ellipse has following parameter, major axis horizontal with length 12, length of minor…

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.