Express the surface x = 5cosθsinφ, y = 6sinθsinφ, z = 4cosφ as a level surface f(x,y,z) = 14400, f(x,y,z) =

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Express the surface x = 5cosθsinφ, y = 6sinθsinφ, z = 4cosφ as a level surface f(x,y,z) = 14400, f(x,y,z) =

Mathematics
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x^2/(5sinφ)^2 + y^2/(6sinφ)^2 =1 (sinφ)^2 =1 - (z/4)^2 substitute for sinφ
x^2/25 + y^2/36 = 1 - (z/4)^2 x^2/25 + y^2/36 + z^2/16 = 1

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Other answers:

multiply by 14400 on both sides
576x^2 + 400y^2 + 900z^2 =14400= f(x,y,z)

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