Find an equation for the paraboloid z=3-(x^2+y^2) in spherical coordinates.
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In spherical coordinates:
ρ cos φ = 3 - [(ρ cos θ sin φ)^2 + (ρ sin θ sin φ)^2]
==> ρ cos φ = 3 - ρ^2 sin^2(φ) (cos^(θ) + sin^2(θ))
==> ρ cos φ = 3 - ρ^2 sin^2(φ).
I hope this helps!
ρ cos φ = 3 - [(ρ cos θ sin φ)^2 + (ρ sin θ sin φ)^2]
==> ρ cos φ = 3 - ρ^2 sin^2(φ) (cos^(θ) + sin^2(θ))
==> ρ cos φ = 3 - ρ^2 sin^2(φ).
I hope this helps!