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?
I need to know what equation to use!
the formula for the reflector is x=1/8 y^2
the location of the focus is 2,0
for the parabola
y^2 = 4px
the vertex is at a distance p from the focus.
How do I find the solution? Is 2 the solution?
I got this far: y^2 = 8x
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
Is this it?
y^2 = 8x
8x = y^2 = 4px
8x = 4px
8 = 4p
8/4 = 4p/4
2 = p