SOLUTION: A SEARCHLIGHT HAS A PARABOLIC REFLECTOR (HAS A CROSS SECTION THAT FORMS A BOWL) THE PARABOLIC BOWL IS 16 INCHES WIDE FROM RIM TO RIM AND 12 INCHES DEEP. THE FILAMENT OF THE LIGHT B

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Question 1120460: A SEARCHLIGHT HAS A PARABOLIC REFLECTOR (HAS A CROSS SECTION THAT FORMS A BOWL) THE PARABOLIC BOWL IS 16 INCHES WIDE FROM RIM TO RIM AND 12 INCHES DEEP. THE FILAMENT OF THE LIGHT BULB IS LOCATED AT THE FOCUS. WHAT IS THE EQUATION OF THE PARABOLA USED FOR THE REFLECTOR? HOW FAR FROM THE VERTEX IS THE FILAMENT OF THE LIGHT BULB?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Middle of the dish sits on origin of cartesian system. Cross section may be y=ax%5E2, and three points are (0,0), (8,12), and (-8,12).

a=y%2Fx%5E2
a=12%2F8%5E2=%284%2A3%29%2F%284%2A2%2A8%29
a=3%2F16

y=%283%2F16%29x%5E2

highlight%28%2816%2F3%29y=x%5E2%29
-
FOCUS AND LOCATION OF BULB
p, distance from vertex to bulb

4p=16%2F3
p=%2816%2F3%29%281%2F4%29
p=4%2F3
Bulb is 1%261%2F3 inches above the vertex or middle point of the satellite dish, in the concave region.