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thank you 

 Oct 9, 2019
 #1
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+1

Let the center of the hyperbola be  at the origin  =  (0,0)

 

We will have this form

 

x^2           y^2

___    -    ____    =  1

a^2           b^2

 

c  = the distance from either of the focal points to the center   =  100  miles

And c^2  = 10000

 

For any point on the hyperbola, the differences of the distances from the two foci  to this point  = 2a

 

So

 

2a  = 180

a  =  90    ⇒   a^2  = 8100

 

And we have that

c^2  = a^2 + b^2

c^2 - a^2  = b^2

10000 - 8100  = b^2

1900  =  b^2

 

So  the equation becomes

 

x^2           y^2

____  -    _____   =      1

8100         1900

 

Here is a graph : https://www.desmos.com/calculator/5dyujkabt4

 

cool cool cool

 
 Oct 9, 2019
edited by CPhill  Oct 9, 2019

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