A lamp with a parabolic reflector is shown in the figure The

A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus, and the focal diameter is 12 cm. Find an equation of the parabola. Find the diameter d(C, D) of the opening, 20 cm from the vertex.

Solution

Lets assume the reflector is placed at origin i.e.vertex is at origin:

Let the focus be at (p,o)

So, one points on parabola are ( p,6) and (p, -6)

equation of parabola: y^2 = 4px

So, 6^2 =4*p*p ----> p^2 = 36/4

p= 3

a) So, y^2 = 12x

b) 20 cm from vertex:

x =20 ; y^2 = 12*20

y =15.49

d(C, D) = 30.08 c m