SOLUTION: What is the standard form of the hyperbola with vertices (1,0),(-1,0) and assymptote of y=5x y=-5x?

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Question 1120056: What is the standard form of the hyperbola with vertices (1,0),(-1,0) and assymptote of y=5x y=-5x?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


With vertices (1,0) and (-1,0), the center is at (0,0), and the branches open right and left. The general form of the equation is

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

The center is (h,k); a is the distance from the center to either vertex, which is 1; b/a and -b/a are the slopes of the two asymptotes.

Since the slopes are 5 and -5, that means b is 5, and we have all the pieces we need to write the equation:

%28x-0%29%5E2%2F1%5E2+-+%28y-0%29%5E2%2F5%5E2+=+1

or

x%5E2-y%5E2%2F25+=+1