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A cross section of the mirror of a flashlight is a parabola. It measures 6 cm across
and has a depth of 2 cm. How far from the vertex should the filament of the light bulb
be placed for the flashlight to have its beam run parallel to the axis of its mirror?
A. 2.667 cm
B. 0.889 cm
C. 1.125 cm
D. 2.25 cm
E. 0.444 cm
F. 0.75 cm
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Place the origin of the coordinate system at vertex of the parabola.
Use the vertex form equation of this parabola
y = . (1)
At x = 3 cm, we are given y = 2 cm. So, this vertex equation takes the form
2 = a*3^2, which gives a = .
So, equation (1) is
y = . (2)
For the parabola with equation y = , the distance from the vertex to the focus is
f = .
In our case, the distance from the vertex to the focus is = cm = 1.125 cm.
ANSWER. The distance from the vertex to the focus, where the filament should be placed, is 1.125 cm.
Option (C).
Solved.