SOLUTION: A searchlight has a parabolic reflector that forms a “bowl” which is 12 inches wide from rim to rim and 8 inches deep. If the filament of the light bulb is located at the focus, ho

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Question 1012198: A searchlight has a parabolic reflector that forms a “bowl” which is 12 inches wide from rim to rim and 8 inches deep. If the filament of the light bulb is located at the focus, how far from the vertex of the reflector is it?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
4py=x%5E2 can be a parabola with vertex at the origin, and opening upward. Using different symbols, the parabola can also be y=ax%5E2 and has points (-6,8) and (6,8).

Find the factor, a.
8=a%2A6%5E2, using the simpler formula.
a=8%2F36
a=2%2F9
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The equation for the parabola more specifically can be highlight%28y=%282%2F9%29x%5E2%29.

What about the focus?
Put the equation with the p into the same form as the more specific-found equation. The value of p is THE DISTANCE FROM VERTEX TO FOCUS.
4py=x%5E2
y=%281%2F%284p%29%29x%5E2
Comparing the corresponding equation parts,
2%2F9=1%2F%284p%29
9%2F2=4p
p=9%2F%282%2A4%29
highlight%28p=9%2F8%29.

The focus will be on the "opening upward" side of the parabola, as described in this discussion, above the origin, so the focus is highlight%289%2F8=1%261%2F8%29 inches away from the vertex. Inside of the curve.