converting cartesian co-ordinations to Polar co-ordination for an ellipse

Question

An ellipse with the equation [((x-1)^2)/9]+[(y^2)/8]=1
Show that the given ellipse in polar co-ordinates has the form a+rcosTheta = br
additionally determine the values of a and b

Answer 1

Plug in x = r cosθ, y = r sinθ,

(r cosθ - 1)²/9 + (r sinθ)²/8 = 1

Multiply both sides by 72,

8(r cosθ - 1)² + 9(r sinθ)² = 72

Simplify,

(rcosθ + 8)² = 9r²

8 + rcosθ = 3r

Compare,

a = 8, b = 3 <==Answer