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9 August, 07:22

Write the equation in spherical coordinates. (a) 4x2 - 3x + 4y2 + 4z2 = 0

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  1. 9 August, 07:45
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    4x^2-3x+4y^2+4z^2=0

    here we shall proceed as follows:

    x=ρcosθsinφ

    y=ρsinθsinφ

    z=ρcosφ

    thus

    4x^2-3x+4y^2+4z^2=

    4 (ρcosθsinφ) ^2-3 (ρcosθsinφ) + 4 (ρsinθsinφ) ^2+4 (ρcosφ)

    but

    ρ=1/4cosθsinφ

    hence we shall have:

    4x^2-3x+4y^2+4z^2

    =1/4cosθsinθ (cosθ (4-3sinφ)) + 4sin^2 (φ)
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