SOLUTION: Find an equation of the hyperbola that has foci at (-15,0) and (15,0), and asymptotes y= 2x and y=-2x

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Question 1173706: Find an equation of the hyperbola that has foci at (-15,0) and (15,0), and asymptotes y= 2x and y=-2x
Found 2 solutions by greenestamps, ewatrrr:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The asymptotes y=2x and y=-2x tell us that the center of the hyperbola is (0,0).

With the foci in the x direction from the center (0,0), the equation is

x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1

The slopes of the asymptotes 2 and -2 tell us that b=2a; so the equation is

x%5E2%2Fa%5E2-y%5E2%2F%284a%5E2%29=1

The distance from the center to each focus, c, is 15; c is related to a and b by

c%5E2+=+a%5E2%2Bb%5E2

c%5E2+=+225+=+a%5E2%2Bb%5E2+=+a%5E2%2B4a%5E2+=+5a%5E2
a%5E2+=+45

The equation is

x%5E2%2F45-y%5E2%2F180+=+1

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Had previously graphed the Hyperbola... thought I would send it along
+x%5E2%2F45+%2B+y%5E2%2F180+=+1