Question

x^2+Y^2+6=0  express in polar cooordinates.

Answer 1

Using polar coordinate transformations

x = r Cosθ

y = r sinθ

Now x^2+y^2+6 = 0

(r Cosθ)^2+(r sinθ)^2+6 = 0

r^2 Cos^2θ+r^2 Sin^2θ+6 = 0

r^2(Cos^2θ+Sin^2θ)+6 = 0

r^2+6 = 0