Euclid's Muse

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Search Results for “parabola”

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

Tags: parabola, focus, circumcircle

By Phil Todd
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

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

By Phil Todd
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

By Phil Todd
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

By Phil Todd
Parabola Polar Line
The locus of the intersection of tangents at the ends of chords of a parabola through a given fixed point is a straight line. This is called the polar line of the given point

Tags: parabola, polar

By Phil Todd
Parabola Directrix
Explore the focus and directrix of a parabola

Tags: parabola, focus, directrix

By Phil Todd
Parabola Parametrization
Investigate the characteristics of the standard parametrization of a parabola.

Tags: parabola, conic-section, parameter

By Phil Todd
Parabola Subnormal
The subnormal for a given parabola is constant, and closely related to the focal length.

Tags: parabola, focus, conic

By Phil Todd
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

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