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Question 744428: A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 7m down from the top of the dome the ceiling is 12m wide, find the best location for the light source.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 7m down from the top of the dome the ceiling is 12m wide, find the best location for the light source.
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Place vertex of dome at (0,0)
coordinates of end-points of 12 ft dome: (-6,-7) and (6,-7)
basic equation of parabolic dome: x^2=-4py
using coordinates of end points:
x^2=-4py
36=-4p(-7)
4p=36/7
p=9/7
best location for the light source: (0,-9/7)
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