Question

A car’s headlight contains a parabolic reflector. A special bulb with two filaments is used to produce
the high and low beams. The filament placed at the focus produces the high beam and the filament
placed off-focus produces the low beam. The equation of the reflector is x=1/8y^2. How far from the
vertex should the filament for the high beam be placed?

Answer 1

I need to know what equation to use!

Answer 2

the formula for the reflector is x=1/8 y^2

the location of the focus is 2,0

Answer 3

for the parabola

y^2 = 4px

the vertex is at a distance p from the focus.

Answer 4

How do I find the solution? Is 2 the solution?

Answer 5

I got this far: y^2 = 8x

Answer 6

so, 8=4p
p=2
that is the distance from the vertex to the focus. All you need to do is

(a) read what we gave you
(b) think about it a bit

Answer 7

Is this it?

y^2 = 8x
8x = y^2 = 4px
8x = 4px
8 = 4p
8/4 = 4p/4
2 = p