Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate.
A = 12 ft, b = 8 ft

A) The focus is 32 in. from the vertex on the axis of the parabola.
B) The focus is 16 in. from the vertex on the axis of the parabola.
C) The focus is 12 in. from the vertex on the axis of the parabola.
D) The focus is 8 in. from the vertex on the axis of the parabola.

Question

Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate. ​
A = 12 ft, b = 8 ft
​  ​
A) The focus is 32 in. from the vertex on the axis of the parabola. 
B) The focus is 16 in. from the vertex on the axis of the parabola. 
C) The focus is 12 in. from the vertex on the axis of the parabola. 
D) The focus is 8 in. from the vertex on the axis of the parabola.

Quizplus · Accepted Answer

The focal length of a parabolic mirror is equal to one-fourth of the distance between the vertex and the focus, i.e. $f=\frac{A}{4}$.
In this case, $A=12$ ft, so $f=\frac{12}{4}=3$ ft.
To convert this to inches, we multiply by 12, giving $f=36$ in.
Thus, the focus is 36 inches from the vertex on the axis of the parabola.
But the question asks for the distance from the vertex to the point where the beams concentrate, which is twice the focal length. 
Therefore, the distance from the vertex to the point where the beams concentrate is $2f=2\cdot 36=\boxed{72}$ inches or 6 feet.

Beams of Light Parallel to the Axis of the Parabolic