Determine Bulb Position for Parabolic Reflector of Headlight

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To determine the bulb position for a parabolic reflector, the focus must be calculated using the given dimensions. The distances from points B to C (32 cm) and A to D (8 cm) are critical for establishing the parabola's geometry. The equation y^2 = 4px is relevant, where p represents the distance from the vertex to the focus. By identifying points B and C on the parabola, the value of p can be solved, leading to the correct bulb placement. Understanding these relationships is essential for accurate positioning of the bulb at the focus.
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The cross section of a parabolic reflector of a headlight is shown in the diagram. The distance from B to C is 32 cm and the distance from A to D is 8 cm. Determine where the builb should be located if it is positioned at the focus.

. ...|...B
. ...|
. ...|
. ...|
----|---------D
. ...|A
. ...|
. ...|
. ...|...C

Remember its a parabola connect the dots.


This is what i have done
x^2/a^2 - y^2/b^2 = 1
then i substituted a as 0 and b as 16 and it got me nowhere
I'm guessing it has to be located at 0 but i don't know how to prove it all i know are these equations...
x^2/a^2 - y^2/b^2 = 1, a^2 +b^2 = c^2 and that's all
(P.S. Latex is hard to learn)
 
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runicle said:
This is what i have done
x^2/a^2 - y^2/b^2 = 1
then i substituted a as 0 and b as 16 and it got me nowhere
I'm guessing it has to be located at 0 but i don't know how to prove it all i know are these equations...
x^2/a^2 - y^2/b^2 = 1, a^2 +b^2 = c^2 and that's all
(P.S. Latex is hard to learn)
The equation for a parabola in this orientation is:

y^2 = 4px where A = (0,0) is the origin and p is the distance from the origin to the focus. The points B = (16, 16), C = (16, -16) are on the parabola. That will enable you to solve for p.

AM
 
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