# Search Results for “parabola”

##### Parabola Tangent Circumcircle

3 tangents of a parabola form a triangle. Its circumcircle passes through the parabola's focus.##### Parabola and catenary

There isn't much difference between a catenary and its approximate parabola. The catenary is the correct model of an ideal chain. But the parabola fits fairly well too.##### Caustic curve as focus of parabola

The red curve is f(x) (for -2≤x≤2). The blue curve is the terms up to the square term of the Taylor series. A is the vertex of this parabola, B is its focus. The orange curve is the caustic - envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.##### Rolling Parabola

If you roll a parabola along the ground, what curve does its focus trace out? It might look like a parabola, but is it?##### Parabola Generalization

A theorem of Archimedes on a circle can be generalized to parabolas as shown here. Vertical lines correspond to diameters of the parabola. FG is parallel to the tangent at C. E is the intersection of the tangents at F and C. Observe that teh vertical line through E bisects FG.##### Parabola Caustic

Rays emanate from D, and their reflections in the parabola form a caustic. See the family of rays by pressing**Show**, then the caustic curve by pressing

**Show**again. You can drag C and D.

##### Polar Point Parabola

The polar point of a line in a parabola is a common point to the chords defined by the common tangents through the points on the line. (Go to**Full Screen**if the green points won’t drag)