WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Parabolic Envelope from Congruent Triangles

​
show labels
Consider a line
l
and a point
P
not on
l
. Drag the orange point
Q
along
l
. Draw a vertical line
m
from
Q
. The perpendicular bisector
k
of
PQ
meets
m
at a point
R
that traces out a parabola and
k
is tangent to the parabola. The focus and directrix of the parabola are
P
and
l
because
△PQR
is isoceles. The part of the vertical line m inside the parabola is the reflection in
k
of the ray
PR
.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.