Question

The mirror in Alan's flashlight is a paraboloid of revolution. If the mirror is 8 centimeters in

diameter and 4.5 centimeters deep, where should the light bulb be placed so it is at the focus

of the mirror?

Answer 1

Answer:

8/9 cm above the Vertex

Step-by-step explanation:

Given that:

Diameter of mirror = 8cm

Depth = 4.5 cm

Assume parabola opens up to the right, then p is positive

y² = 4px

Point on the parabola will then be ;

(Depth, d/2) = (4.5, 4)

x = 4.5 ; y = 4

4² = 4p(4.5)

16 = 18p

p = 16/18

p = 8/9

Hence, bulb should be placed 8/9 cm above the Vertex