Consider a line
and a point
not on
. Drag the orange point
along
. Draw a vertical line
from
. The perpendicular bisector
of
meets
at a point
that traces out a parabola and
is tangent to the parabola. The focus and directrix of the parabola are
and
because
is isoceles. The part of the vertical line m inside the parabola is the reflection in
of the ray
.
