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Question 40296: a hyperbolic mirror can be usedto take panoramic photographs. A camera is pointed toward the vertex of the mirror and is positioned so that the lens is at one focus of the mirror. An equation for the cross section of the mirror is x squared/ 25 minus 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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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