Chapter 10, Problem 11RE

In each part, identify the curve by converting the polar equation to rectangular coordinates. Assume that $a>0.$

$\begin{array}{l}\left(\text{a}\right)r=a{\sec }^2\frac{\theta }{2}\\ \left(\text{b}\right)r^2\cos 2\theta =a^2\\ \left(\text{c}\right)r=4\csc \left(\theta -\frac{\pi }{4}\right)\\ \left(\text{d}\right)r=4\cos \theta +8\sin \theta \end{array}$