Cycloid Family

To Try: Start by sliding t and watch the circle roll. Pay attention to point P.
Check box "show curve" to mark the path of P.
r is a radius of the circle and p is the position of P on the radius ray.

A Challenge: Assuming that r is the length of the radius of the generating circle, and p is the distance from point P to the origin, develop equations for x(t) and y(t).

bic, Created with GeoGebra