math help

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