# Hypocycloid degenerates to straight line

Can someone please explain if the hypocycloid described below would degenerate to a line. If possible, can someone provide an actual plot of the entire question?

The scenario is as follows:

A circle starts rolling on a flat surface. After it completes one revolution, the path starts curving up in the arc of a circle till it becomes vertical and then the path becomes vertical. During the curved part of the path, the circle performs exactly half a revolution and then completes the other half of the revolution on the vertical path. Plot the locus of the point which was initially in contact the ground.

EDIT: The problem is 2-D. Everything happens in a plane (I've copied the question exactly, except the original asks you to plot on paper). By vertical, it actually means upwards, parallel to the vertical edge of the paper and similarly for horizontal.

• What is the question you refer to? Also, this would probably be more appropriate at math.stackexchange.com – atom44 Aug 11 '16 at 9:07
• PLEASE READ THE FULL QUESTION, THE QUESTION IS WRITTEN BELOW!! Thanks for the tip anyway! – pulsejet Aug 11 '16 at 12:28