Answer
Circular cylinder centered at the x-axis with radius $3$.
Work Step by Step
Conversion of rectangular to spherical coordinates is as follows:
$x=\rho \sin \phi \cos \theta; y=\rho \sin \phi \sin \theta;z=\rho \cos \phi$
and
$\rho=\sqrt {x^2+y^2+z^2}$;
$\cos \phi =\dfrac{z}{\rho}$; $\cos \theta=\dfrac{x}{\rho \sin \phi}$
Here, $\rho^2( \sin^2 \theta \sin^2 \phi+\cos^2 \phi) =9$
This implies that
$\rho^2 \sin^2 \theta \sin^2 \phi+\rho^2 \cos^2 \phi) =9$
or, $y^2+z^2=9$
or, $y^2+z^2=3^2$
Hence, the given equation shows a circular cylinder centered at the x-axis with radius $3$.
