## University Calculus: Early Transcendentals (3rd Edition)

a) $r=a \sec \theta$ b) $r=b \csc \theta$
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: $r=b \csc \theta$