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Question 77348: A searchlight is shaped like a paraboloid of revelution. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be? Assume the light source is at the parabola's focus.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A searchlight is shaped like a paraboloid of revelution. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be? Assume the light source is at the parabola's focus.
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Draw the picture of the parbola opening upward with vertex at (0,0)
and focus at (0,3).
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Form: x^2=4py
Distance from vertex to focus = p=3
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Equation: 12y=x^2
y=(1/12)x^2
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If the opening is 12 feet across it intersects the parabola at (-6,y) and (6,y)
Need to find y to get the depth of the light.
y=(1/12)(6^2)=3
So the depth is 3 ft.
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Cheers,
Stan H.
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