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CYCLOID animation のコピー

The CYCLOID is traced by a point on the circumference of a circle which ROLLS without slipping over a straight line.
1.What are the parametric equations of a CYCLOID ? 2. What if the generating line is shifted above the circle ? What changes are to be made in the Parametric equations in that case ? 3. Also if the Cycloid is to have a phase shift , how would its equation change in that case ?