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P Take a Test Joshua gibson Google Chrome https:// 1230987348 centerwin yes&fromPlayerCheck; yes Joshua gibson 3/7/16 5:53 PM Quiz: Quiz #4 9.2 9.4, 9.7 Overview 11 12 13 14 15 4 of 15 complete This Question: 1 pt This Test: 15 pts A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be? The searchlight should be feet deep. (Type an exact answer in simplified form.) Enter your answer in the answer box. Previous Question Next Question I Submit Quiz 553 PM HE Search the web and Windows 3/7/2016

Solution

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 (0,2).
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Form: x^2=4py
Distance from vertex to focus = p=2
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Equation: 8y=x^2

y=(1/8)x^2
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If the opening is 12 feet across it intersects the parabola at (-4,y) and (4,y)
Need to find y to get the depth of the light.
y=(1/8)(4^2)=2
So the depth is 2 ft.