We have been given the equation in rectangular coordinates as
[tex]x^2+y^2+z^2-3z=0[/tex]
In Spherical coordinates, we know that
[tex]x=\rho \sin \phi \cos \theta\\ y=\rho \sin \phi \sin \theta\\ z=\rho \cos \phi\\ x^2+y^2+z^2=\rho^2[/tex]
On substituting these values in the given equation, we get
[tex](x^2+y^2+z^2)-3z=0[/tex]
[tex]\rho^2- 3\rho \cos \phi=0\\ \\ \rho^2= 3\rho \cos \phi\\ \\ \rho = 3 \cos \phi[/tex]
Thus, the equation in spherical coordinates is given by
[tex]\rho = 3 \cos \phi[/tex]
