spherical parametrization

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spherical parametrization for different equations

A=$x^2+y^2+z^2=5, z\geq0.$

B=$(x-1)^2+(y-1)^2+z^2=1.$

C=$2x^2+3y^2+4z^2=1.$

for A i know that the answer would be

$r\left(\theta,\phi\right)=\left[\rho\sin\phi\cos\theta,\rho\sin\phi\sin\theta,\rho\cos\phi\right]$ where $\rho=\sqrt{5}$

B is a spherical coordinates centered at (1,1,0)

but what are the changes that i must do to solve B and C

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HINT:

for B, $$x-1=\sin\phi\cos\theta,y-1=\sin\phi\sin\theta,z=\cos\phi$$

and for C,$$\sqrt2x=\sin\phi\cos\theta,\sqrt3y=\sin\phi\sin\theta,2z=\cos\phi$$