OCR A Level: Further Pure 2 - Polar Coordinates [June 2013 Q8]

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 .