Answer
(a) See explanations.
(b) See graph.
Work Step by Step
(a) Use the figure given in the Exercise:
Step 1. With a diameter $2a$ and angle $\theta$, we have $OC=\frac{2a}{sin\theta}$.
Step 2. Find the length of OA as $OA=2a\cdot sin\theta$
Step 3. Find the coordinates of P(x,y): $x=OC\cdot cos\theta=$ and $y=OA\cdot sin\theta$
Step 4. Combine the above results to get the parametric equations as:
$x=\frac{2a}{sin\theta} cos\theta=2a\cdot cot\theta$
$y=2a\cdot sin\theta\cdot sin\theta=2a\cdot sin^2\theta$
(b) See graph.
