# Euclid's Muse

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# Search Results for “parabola”

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

Tags: parabola, focus, circumcircle

##### 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.

Tags: parabola, catenary

##### 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.

Tags: caustic, Taylor-series, parabola

By Duncan
##### 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?

Tags: parabola, catenary, focus

##### Parabola Directrix
Explore the focus and directrix of a parabola

Tags: parabola, focus, directrix

##### Parabola Generalization
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.

Tags: parabola, Archimedes

##### 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.

Tags: caustic, parabola

##### 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)

Tags: polar, parabola

##### Focus Directrix Parabola
Try to set the focus and directrix of a parabola so it matches one with a given equation

Tags: parabola, focus, directrix

##### Parabola Parametrization
Investigate the characteristics of the standard parametrization of a parabola.

Tags: parabola, conic-section, parameter