Let
P
(
x
1
,
y
1
)
be a point on the parabola
y
2
=
4
p
x
with focus
F
(
p
,
0
)
.
Let
α
e the angle between the parabola and the line segment FP, and let
β
be the angle between the horizontal line
y
=
y
1
and the parabola as in the figure. Prove that
α
=
β
. (Thus, by a principle of geometrical optics, light from a source placed at F will be reflected along a line parallel to the x-axis. This explains why paraboloids, the surfaces obtained by rotating parabolas about their axes, are used as the shape of some automobile headlights and mirrors for telescopes.)