The equation of a curve is \(x^2+y^2-x=\sqrt{x^2+y^2}\).

\((\text{i})\) Find the polar equation of the curve in the form \(r=f(\theta)\).

\((\text{ii})\) Sketch the curve.

\((\text{iii})\) The line \(x+2y=2\) divides the region enclosed by the curve into two parts. Find the ratio of the two areas. (If the ratio is \(a:b\) in its simplest form, input \(a+b\) as your answer.)

There are **3** marks available for part (i), **2** marks for part (ii) and **6** marks for part (iii). In total, this question is worth **15.3%** of all available marks in the paper.

This is part of the set OCR A Level Problems.

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