Answer
(a) $x=a\cdot cos\theta, y=b\cdot sin\theta$
(b) See graph.
(c) $(\frac{x}{a})^2+(\frac{y}{b})^2=1$
Work Step by Step
(a) Use the figure given in the Exercise, as point P forms a right angle as shown in the figure, its x and y coordinates can be written as $x=a\cdot cos\theta, y=b\cdot sin\theta$ which gives the parametric equation.
(b) See graph.
(c) Use the Pythagorean Identify $cos^t+sin^t=1$, the equations in (a) becomes $(\frac{x}{a})^2+(\frac{y}{b})^2=1$ which indicates an ellipse.
