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Question 620450: The filament of a light bulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends light out in a straight beam. Given that the filament is 2 inches from the vertex, find an equation for the cross-section of the reflector. If the reflector 6 inches wide, how deep is it?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The filament of a light bulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends light out in a straight beam. Given that the filament is 2 inches from the vertex, find an equation for the cross-section of the reflector. If the reflector 6 inches wide, how deep is it?
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Horizontal parabola has the form:
x = 1/(4c)(y-k)^2 + h
Since the focus is 2 inches from the vertex
c = 2
and, we can assume the vertex is at (0,0)
x = 1/(4*2)(y-0)^2 + 0
x = 1/8y^2 (equation for the cross-section)
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if the reflector is 6 inches wide then
y = 3
x = 1/8y^2
x = 1/8(3)^2
x = 1/8(9)
x = 9/8 inches
or
x = 1 and 1/8 inches deep
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