SOLUTION: A panoramic photo can be taken using a hyperbolic mirror. The camera is pointed toward the vertex of the mirror and the camera's optical center is positioned at one focus of the mi

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Question 1176578: A panoramic photo can be taken using a hyperbolic mirror. The camera is pointed toward the vertex of the mirror and the camera's optical center is positioned at one focus of the mirror (see figure). An equation for the cross-section of the mirror is x^2/64 − y^2/49 = 1.
Find the distance from the camera's optical center to the mirror. (Round your answer to three decimal places.)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2F64+%E2%88%92+y%5E2%2F49+=+1
=>a%5E2=64
=>b%5E2=49
The formula to determine the focus of a parabola is just the pythagorean theorem.
c%5E2+=a%5E2+%2B+b%5E2.......c is the distance to the focus
c%5E2+=64+%2B+49
c%5E2+=113
focus at
(-sqrt%28113%29, 0) or (sqrt%28113%29, 0)
≈(-10.630, 0) or (10.630, 0)
the distance from the camera's optical center to the mirror is 10.630

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The answer by @MathLover1 is  DEFINITELY  NOT  that you need,  since her
            solution/answer relates to a  PARABOLIC --- not  HYPERBOLIC  mirror.


First,  you need an idea on how this panoramic photo system works.



For it,  read from this source

https://www.researchgate.net/figure/Creation-of-perspective-and-panoramic-images-by-projecting-the-acquired-image-into_fig6_26427604



After that,  look into these sources


https://www.claytonschools.net/cms/lib/MO01000419/Centricity/Domain/204/2_13.pdf

https://www.numerade.com/questions/panoramic-photo-a-panoramic-photo-can-be-taken-using-a-hyperbolic-mirror-the-camera-is-pointed-towar/

https://www.bartleby.com/solution-answer/chapter-93-problem-56e-precalculus-with-limits-a-graphing-approach-7th-edition/9781305071711/photography-a-panoramic-photo-can-be-taken-using-a-hyperbolic-mirror-the-camera-is-pointed-toward/387a4e9b-31c4-4825-ac61-e1e059c2485c


where you will find solutions for  VERY  SIMILAR T WIN  problems.


Without knowing how this panoramic photo system works,  you will not be able to understand  how to solve the problem correctly.