Euclid's Muse

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Search Results for “conic”

By Phil Todd
Ellipse as locus of circle center
Take two overlapping circles.  Examine the locus of the center of the circles tangential to both. It seems to be an ellipse with foci at the centers of the two circles. Prove it.

Tags: ellipse, conic, focus

By Phil Todd
Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.

Tags: polar, conic, hyperbola

By Phil Todd
Ellipse Parametrization
We examine a standard parametrization of an ellipse.

Tags: ellipse, conic-section, parametrization

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

Tags: parabola, conic-section, parameter

By Phil Todd
Polar Line
The locus of the intersections of the tangents at the end of chords of an ellipse which pass through a common point is a straight line. A bit of a mouthful, but play with the diagram and it will become clear.

Tags: locus, polar, ellipse, conic

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 Duncan
String Art
Examine the parabola created in a simple string art figure.  

Tags: parabola, conic

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