SOLUTION: A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the mirror with the lens at one focus of the hyperbola. write the equation of the hyperbo

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Question 712593: A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the mirror with the lens at one focus of the hyperbola. write the equation of the hyperbola that can be used to model a mirror that has a vertex 4 inches from the center of the hyperbola and a focus 1 inch in front of the surface of the mirror. assume the mirror has a horizontal trasverse axis and the hyperbola is centered at (0,0).
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A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the mirror with the lens at one focus of the hyperbola. write the equation of the hyperbola that can be used to model a mirror that has a vertex 4 inches from the center of the hyperbola and a focus 1 inch in front of the surface of the mirror. assume the mirror has a horizontal trasverse axis and the hyperbola is centered at (0,0).
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Standard form of equation for a hyperbola with horizontal transverse axis:
%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center
For given problem:
center: (0,0)
vertices
a=4
a^2=16
..
Foci
c=5
c^2=25
..
c^2=a^2+b^2
b^2=c^2-a^2=25/16=9
..
Equation of hyperbola:
x%5E2%2F16-y%5E2%2F9=1