## Calculus: Early Transcendentals 8th Edition

a) $z^2=2r^2-4$ b) $z=1-2 r\cos \theta+r \sin \theta$
a) We know that in the cylindrical co-ordinates $r^2=x^2+y^2 \implies r=\sqrt{x^2+y^2}$ and $x=r \cos \theta \\ y=r \sin \theta$ Thus, we have $2(x^2+y^2)-z^2=4$ Thus, it can be written as: $2r^2-z^2=4$ or, $z^2=2r^2-4$ b) We know that in the cylindrical co-ordinates $r^2=x^2+y^2 \implies r=\sqrt{x^2+y^2}$ and $x=r \cos \theta \\ y=r \sin \theta$ Thus, we have $2r\cos \theta-r\sin \theta+z=1$ Thus, it can be written as: $z=1-2 r\cos \theta+r \sin \theta$