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ρ = 4sinφcosθ converts very readily to (x-2)

^{2}+ y

^{2}+ z

^{2}= 4 with very little effort.

Now this similar equation looks to me like it should also be a sphere, but I can't seem to get anywhere with it:

ρ = 4sinθcosφ

I just end up with a very ugly

x

^{2}+ y

^{2}+ z

^{2}= 4yz/(√(x

^{2}+y

^{2})

and I have no idea what to do with that.

Is this a dead end? Is the second equation not a sphere?