Chapter 10.2, Problem 59ES

(a) Show that if a varies, then the polar equation $r=a\sec \theta \left(-\pi /2<\theta <\pi /2\right)$ describes a family of lines perpendicular to the polar axis.

(b) Show that if b varies, then the polar equation $r=b\csc \theta \left(0<\theta <\pi \right)$ describes a family of lines parallel to the polar axis.