A point C on a cycloid and its corresponding cycloidal evolute point E are made during rolling of its generating circle on x-axis.
If a point P divides CE so that CP/CE = k, find the locus of P.
They appear to be also epi- and hypo-cycloids, but am not sure without some more computation work. Required is the line on which the P-circle rolls and its crank radius. When k = 1/2, P-locus is a straight line parallel to x-axis.
Please upload its sketch. This is n't a class exercise.