SOLUTION: A hyperbola has vertices (1,9) and (13,9), and one of its foci is (−2,9). Find its standard equation.

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Question 1180954: A hyperbola has vertices (1,9) and (13,9), and one of its foci is (−2,9). Find its standard equation.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The transverse axis (between the two vertices) is horizontal, so the branches of the hyperbola open left and right; the general equation is

%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1

The center is halfway between the two vertices, at (7,9).

a is the distance from the center to either vertex, so a=6; a^2=36.

c is the distance from the center to either focus, so c=9; c^2=81.

b^2=c^2-a^2=45

ANSWER: %28x-7%29%5E2%2F45-%28y-9%29%5E2%2F36=1