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Vertices (7,5) and (7,-1) Foci (7,7) and (7,-3)

2006-11-07 15:12:09 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

Since the foci of this hyperbola both lie on the horizontal line y=7, then the major axis is horizontal and the minor axis is vertical, and so the equation for it is

((x-a)^2)/(M^2) - ((y-b)^2)/(m^2) = 1

where the center of the hyperbola (the midpoint of the segment between the two foci) is (a,b), M is the length of the semi-major axis (half the distance between the vertices), and m is the length of the semi-minor axis. If d is half the distance between the foci, then M^2 + m^2 = d^2
The center of this hyperbola is (7,2) since it is the midpoint of the segment between the foci. M = 3 (the distance from the center to each vertex), d = 5 (the distance from the center to each focus), and so m = 4 since 3^2 + 4^2 = 5^2.

Thus this hyperbola has equation

((x-7)^2)/9 - ((y-2)^2)/16 = 1

2006-11-07 15:48:15 · answer #1 · answered by wild_turkey_willie 5 · 0 0

...that makes 0 sence...sorry

2006-11-07 23:27:10 · answer #2 · answered by Anonymous · 0 0

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