## Thomas' Calculus 13th Edition

$x^{2}+y^{2}=16,\qquad z=3$
Plane: perpendicular to the z-axis $\Rightarrow$ parallel to the xy-plane ($z=0)$ Passes through a point in which $z=3 \Rightarrow$ the plane is $z=3$ . Sphere:$\qquad x^{2}+y^{2}+z^{2}=25$ Substitute z=3 into the equation for the sphere, $x^{2}+y^{2}+9=25,\qquad z=3$ $x^{2}+y^{2}=16,\qquad z=3$ (circle of radius 4 in the plane $z=3$, centered on the z-axis).