Question

The role a searchght is in the shape of a paraboloid of revolution its diameter is 40 inches and its depth is 20 inches How far from the should the light bulb be placed Themes will be relected parallel to the ads of symmetry if the bubis placed at the focus of the parabola Find the coordinates of the focus Skatch the paran ned to form the reflector on a rectangula coordinate systems that the part of the part the locus is on the positive is the origin and it opens up so The equation of the parabola has the form X = day and its focus is at (D ) Use the fact that the reflector is 10 inches wide and 20 inches doup to determine the coordinates of a point on the parabola. Notice that the x-coordinate of the point is half of the width of the rotector and they coordinate is the depth P0.20) Since the point 2020) is on the graph.satisfies the equation of the parabole Substate 20 forxan gowtion and so for = 4 7 1201 Substitute The focus is the point 51 The light bubhould be placed 5 inches from the vortex

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Answer 1

the equation of parabola is of the form x2 = 4ay and its focus is at (0,a)

the reflector is 40 centimeters wide and 25 centimeters deep. the x coordinate of P is half the width of reflector and y coordinate is the depth.

P = (20,25)

since P is on the graph it satisfies the equation of parabola thus

202=4a25

a=4 thus the light bulb should be placed 4cm from vertex