Answer
(a) $x=\frac{a}{cos\theta}, y=b\cdot sin\theta$
(b) See graph.
Work Step by Step
(a) Use the figure given in the Exercise, as $AB$ is the tangent to the larger circle, we have $\angle OAB=90^{\circ}$ and we have $cos\theta=\frac{OA}{OB}=\frac{a}{x_P}$ so that $x_P=\frac{a}{cos\theta}$. We also know that $y_P=b\cdot sin\theta$, so we have the parametric equations $x=\frac{a}{cos\theta}, y=b\cdot sin\theta$
(b) See graph.
