ParabolaCentersTangentCircles

Parabolas through tangent circles

The two parabolas below are defined as the locus of centers of circles tangent to a given line (the x-axis) and a given circle (c(C,r)).
The figure describes the construction of the two circles which are tangent to the line at point X and also tangent to (c).
The blue/pink parabola is the locus of the centers of the solution-circles which are tangent to c externally/internally.

The calculation below leads to the representation of the blue parabola as a graph of a quadratic function y=px² + q.

The calculation below leads to the representation of the pink parabola as a graph of a quadratic function y=px² + q. It is essentially the same with the previous one differing from it only in a few sign changes.

Parabolas through tangent circles

See Also