SOLUTION: A hyperbolic mirror (used in some telescopes) has property that a light ray directed at a focus will be reflected to the other focus. The focus of a hyperbolic mirror can be repres

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Question 256816: A hyperbolic mirror (used in some telescopes) has property that a light ray directed at a focus will be reflected to the other focus. The focus of a hyperbolic mirror can be represented on a rectangular coordinate system by coordinates (24,0). Find the vertex of the mirror if the Mount at the the top edge of the mirror has coordinates (24,24). Sketch the focus, vertex, and part of the hyperbola to represent the mirror. Can you explain this?
Found 2 solutions by drk, ikleyn:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Vertex = (0,0)
Focus = (24,0)
point on parabola = (24,24)
The general equation is
(i) y+=+a%28x-h%29%5E2+%2B+k
or
(ii) y+=+%281%2F4p%29%28x-h%29%5E2+%2B+k
From the given information, we get
(iii) y+=+a%28x-+0%29%5E2+%2B+0
or
(iv) y+=+ax%5E2
Now we have the coordinate 24,24, so (iv) becomes
(v) 24+=+a%2824%29%5E2
solving for a, we get
a+=+1%2F24
So, our answer is
y+=+%281%2F24%29x%5E2

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

The goal of my post is to  DISPROVE  the solution by other tutor,
given long time ago  (probably,  20  years ago).


The problem is about hyperbolic mirror,  but the other tutor solves it for parabolic mirror,
without any explanations,  why he  (or she)  solves different problem.


So,  ignore that solution as  IRRELEVANT.


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I looked at other solutions of this tutor and noticed that they are quite accurate
and are written in good style;  so,  this case looks like a random accident . . .