A searchlight reflector is designed so that a crass section through its axis is
a parabola and the light source is at the focus. Find the focus if the
reflector is 3 feet across the opening and 1 foot deep.
Where do I even start?!? I'm so lost!
The equation of a parabola whose vertex is at the origin (0,0) is
x² = 4py
where p is the distance from the vertex (0,0) to the focus.
The parabola must go through the points (±3/2,1) in order to be 3 feet across
and 1 foot deep. Substituting ±3/2 for x and 1 for y:
(±3/2)² = 4p(1)
9/4 = 4p
Solve for p by dividing both sides by 4, and 9/4 divided by 4 = 9/16, so
p = 9/16 feet, or converting to inches 6 3/4 inches from the
So the focus is 6 3/4 inches above the vertex and 5 1/4 inches below glass.
Edwin
AnlytcPhil@aol.com
