The vertices of the hyperbola with equation 922 – 72x – 16y? – 128y – 256 = 0 are the foci of an ellipse that contains the point (8, –10). Find the standard equation of the ellipse. O (z! 4)2 (y–4)² 48 64 O (2-4)2 (y: 4)² = 1 64 48 O (2+4)? (y-4)² 1 16 O (x-4)? (y: 4)2 1 %3D 16

The vertices of the hyperbola with equation 922 – 72x – 16y? – 128y – 256 = 0 are the foci of an ellipse that contains the point (8, –10). Find the standard equation of the ellipse. O (z! 4)2 (y–4)² 48 64 O (2-4)2 (y: 4)² = 1 64 48 O (2+4)? (y-4)² 1 16 O (x-4)? (y: 4)2 1 %3D 16

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 56E

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Question

The vertices of the hyperbola with equation 922 – 72x – 16y? – 128y – 256 = 0 are the foci of an ellipse that
contains the point (8, –10). Find the standard equation of the ellipse.
O (z! 4)2
(y–4)²
48
64
O (2-4)2
(y: 4)²
= 1
64
48
O (2+4)?
(y-4)²
1
16
O (x-4)?
(y: 4)2
1
%3D
16

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An ellipse is the set of all points in the plane for which the ____ of the distances from two fixed points F1 and F2 is constant. The points F1 and F2 are called the ____ of the ellipse.

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