Answer
a) $r=a \sec \theta$
b) $r=b \csc \theta$
Work Step by Step
a) Since, we have $x=r \cos \theta$ and $y=r \sin \theta$ and $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
Every vertical line in the xy-plane has the form of $x=a$, so: $r \cos \theta=a$
The polar equation can be rearranged as: $r=a \sec \theta$
b) Since, we have $x=r \cos \theta$ and $y=r \sin \theta$ and $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
Every horizontal line in the xy-plane has the form of $y=b$, so: $r \sin \theta=b$
The polar equation can be rearranged as: $r=b \csc \theta$
