Tchirnhausen's Cubic

The caustic formed by light projecting perpendicular to the axis of a parabola is called Tchirnhausen's Cubic. What happens when the light projects at some other angle?

Tags: Parabola, caustic

And the envelope please...

What is the phantom curve you see when you look at a set of lines, perpendicular to a set of chords through a common point in a circle?

Tags: envelope, circle, ellipse, hyperbola