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

a) $x^2+(y-2)^2=4 ; z=0$ b) $(y-2)^2+z^2=4; x=0$ c) $x^2+z^2=4; y=2$
Definition: The equations of a circle having radius $r$ with center at $(x_0,y_0,z_0)$ are represented as: 1) when the equation of a circle lies in a plane parallel to the $xy$ plane then, we have $(x-x_0)^2+(y-y_0)^2=r^2$; $z=z_0$ 2) when the equation of a circle lies in a plane parallel to the $yz$ plane then, we have $(y-y_0)^2+(z-z_0)^2=r^2$; $x=x_0$ 3) when the equation of a circle lies in a plane parallel to the $xz$ plane then, we have $(x-x_0)^2+(z-z_0)^2=r^2$; $y=y_0$ Thus, we have: a) $x^2+(y-2)^2=4 ; z=0$ b) $(y-2)^2+z^2=4; x=0$ c) $x^2+z^2=4; y=2$