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

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} = 9r^{2}

8 + rcosθ = 3r

Compare,

a = 8, b = 3 <==Answer