parabola envelope

We use a trick to let the trace "open up" as you drag a point. The trick is this:  an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies. Now hide the original point and create another point with parameter t, and make it draggable. Dragging the new point changes the value of t and we see a trace from 0 to t.  

Tags: parabola, envelope

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

Coffee Cup Caustic

You can move the light source and observe the changes in the reflected rays which form the caustic.

Tags: caustic, envelope, reflection, circle

Focal Triangle

Create a triangle which has 3 points on the circumference of an ellipse, and two sides passing through the foci.  Look at 2 curves formed by the third side: the locus of its center and its envelope.  One is an ellipse, the other is not.

Tags: ellipse, focus