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Question 556705: Constructing a headlight: A sealed-beam headlight is in the shape of the a paraboloid of revolution. The bulb, which is placed at the focus is 1 inch from the vertex. If the depth is to be 2 inches, what is the diameter of the headlight at its opening?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Constructing a headlight: A sealed-beam headlight is in the shape of the a paraboloid of revolution. The bulb, which is placed at the focus is 1 inch from the vertex. If the depth is to be 2 inches, what is the diameter of the headlight at its opening?
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Standard form of equation for parabola: x^2=4py (parabola opens upwards)
Headlight parabola:
Set vertex at (0,0)
axis of symmetry: x=0 or y-axis
p=1 (distance from vertex to focus on axis of symmetry)
4p=4
Equation: x^2=4y
At edge of opening, y=2 (depth)
x^2=4*2=8
x=±√8
ans:
Diameter of headlight at opening=2x=2√8
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