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

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

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1 Answer

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