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Search Results for “locus”

By Phil Todd
Ellipse Incenter Locus
What is the locus of the incenter of the triangle formed by the string in the "two pins and a piece of string" construction of an ellipse?

Tags: ellipse, locus

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
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 Duncan
If we look beyond the circumference, what path does a point attached to a rolling wheel take?

Tags: Cycloid, curve, locus

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
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
proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.

Tags: ellipse, focus

By Duncan
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

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