Search Results for “locus”
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?
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.
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.
Cycloid
If we look beyond the circumference, what path does a point attached to a rolling wheel take?
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
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.
proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.
