SOLUTION: A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.

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Question 1141674: A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine a parabola with vertex at (0,0) and points (38, 42) and (-38, 42). Can you work with that, find the equation, and go all the way to the solution?






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y-0=a%28x-0%29%5E2
y=ax%5E2
a=y%2Fx%5E2
a=42%2F%2838%29%5E2
a=%282%2A3%2A7%29%2F%282%2A19%2A2%2A19%29
a=21%2F%282%2A19%5E2%29
a=21%2F722
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y=%2821%2F722%29x%5E2
highlight_green%28%28722%2F21%29y=x%5E2%29
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If p is distance from vertex to focus, then 4p=722%2F21;
p=722%2F%284%2A21%29
p=361%2F21
highlight%28p=17%264%2F21%29
OR
highlight%28p=17.19%2Ainches%29