Chapter 10 - Section 10.3 - Polar Coordinates - 10.3 Exercises - Page 692: 21

$r=\sqrt 7$

$x^{2}+y^{2}=7$ $x=r\cos \theta$ $y=r\sin\theta$ $x^{2}+y^{2}=r^{2}\cos ^{2}\theta+r^{2}\sin^{2}\theta$ $=r^{2}(\cos^{2}\theta+\sin^{2}\theta)=7$ $\cos^{2}\theta+\sin^{2}\theta=1\implies $ $r^{2}=7$ or $r=\sqrt 7$