## Calculus 8th Edition

The conversion of rectangular coordinates to spherical coordinates is given as: $x=\rho \sin \phi \cos \theta; y=\rho \sin \phi \sin \theta;z=\rho \cos \phi$ Here, $\rho=\sqrt {x^2+y^2+z^2}$; $\phi =\cos^{-1} [\dfrac{z}{\rho}]; \theta=\cos^{-1}[\dfrac{x}{\rho \sin \phi}]$ Here, we have $\rho^2-3\rho+2=0$ This gives: $(\rho-1)(\rho-2)=0 \implies \rho=1,2$ The value of $\rho=1$ shows a sphere centered at the origin having radius $1$ and the value of $\rho=2$ shows a sphere centered at the origin having radius $2$. Thus, the given equation shows a pair of concentric spheres.