Question 40296
x squared/ 25 - y squared/ 9 = 1 , where x and y are measured in inches. If you place a camera with lens at the focus, how far is the lens from the vertex of the mirror?

a^2=25; b^2=9
c^2=a^2+b^2 for a hyperbola.
c=sqrt(34)

Your hyperbola is centered at (0,0)
The vertex is at (a,0)=(5,0)
The focus is at (c,0)=(sqrt34,0)
Distance from vertex to focus is 
d=c-a= sqrt(34) - 5 = 0.831 inches
Cheers,
Stan H.