Answer
(a) For a full turn from $0$ to $2\pi$, the satellite orbit the Earth in an ellipse.
(b) $\theta=\pi$, $540mi$
Work Step by Step
(a) See graph, the blue circle represents the Earth and the red oval shaped curvature represents the orbit of the satellite. When $\theta=0$ the satellite is at a furthest point from the Earth, when $\theta=\pi$ the satellite is at its closest point to the Earth. For a full turn from $0$ to $2\pi$, the satellite orbit the Earth in an ellipse.
(b) As mentioned above, when $\theta=\pi$, the satellite is at a position closest to the Earth, and this distance or height of the satellite is given by $r=\frac{22500}{4+1}=4500mi$ at a height of $h=4500-3960=540mi$
