Question 702146
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 5 m down from the top of the dome ceiling is 3 m wide, find the best location for the light source.
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Draw a parabola facing down with the vertex (top of the dome) at the origin (0,0)
Equation for this parabola: x^2=-4py
Using coordinates (1.5,-5), 5 m down from the top where the ceiling is 3 m wide,
x^2=4py
1.5^2=-4p(-5)
2.25/5=4p
4p=0.45
p=0.1125
location for the light source: 0.1125 m below the dome(vertex) on the axis of symmetry(x=0)