Where should the bulb go in a parabolic headlight reflector?

[runicle]

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)

 

[Andrew Mason]

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