SOLUTION: 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 pla
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-> SOLUTION: 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 pla
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Question 1206394: 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 Found 2 solutions by ikleyn, MathLover1:Answer by ikleyn(52776) (Show Source):
You can put this solution on YOUR website! .
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).
You can put this solution on YOUR website!
Its diameter is and its depth is
for simplicity, let vertex be at (,)
parabola opens to the right, and we use the standard equation in the form
where focus is at
two points on this parabola are (,) and (,) => diameter is , above and below x-axis and depth is
using one point we can calculate
