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The point $(8,2)$ is on an asymptote of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1.$ What is $|a/b|$?

 Dec 9, 2018
 #1
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The center is (0,0)

 

The since (8,2) is on the graph....the equation of the asymptote will have a  positive slope...so....

 

y = (b / a) x        and we know that  (x, y)  = (8, 2)....so....

 

2 = (b / a) (8)

 

2/8 = (b / a)

 

1/4 =  b / a        which implies that

 

4 /1  =  a / b   =   4

 

 

cool cool cool

 Dec 9, 2018

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