document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #55468 by stanbon(75887) $\"\"$ $\"About$

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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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\n" ); document.write( "Draw the picture of the parbola opening upward with vertex at (0,0)
\n" ); document.write( "and focus at (0,3).
\n" ); document.write( "---------
\n" ); document.write( "Form: x^2=4py
\n" ); document.write( "Distance from vertex to focus = p=3
\n" ); document.write( "--------
\n" ); document.write( "Equation: 12y=x^2
\n" ); document.write( "y=(1/12)x^2
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\n" ); document.write( "If the opening is 12 feet across it intersects the parabola at (-6,y) and (6,y)
\n" ); document.write( "Need to find y to get the depth of the light.
\n" ); document.write( "y=(1/12)(6^2)=3
\n" ); document.write( "So the depth is 3 ft.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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