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

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)