Further Mathematics 9231: Polar coordinates Topical Past Paper Questions

The curve $C$ has polar equation $r^{2}=\theta\sec^{2}\theta$, where $0\leqslant\theta\leqslant\frac{1}{3}\pi$. (a) Sketch C and state the greatest distance of a point on C from the pole. (b) Find the exact value of the area of the region bounded by $C$ and the half-line $\theta…

The curve $C$ has polar equation $r = e^{\frac{4}{3}\theta}$ for $0 \leqslant \theta \leqslant \pi$. Find the length of $C$. Give your answer in an exact form. [4]

(a) Show that the curve with Cartesian equation $$ \left(x^{2}+y^{2}\right)^{2}=6xy $$ has polar equation $ r^{2}=3\sin2\theta $. The curve C has polar equation $ r^{2}=3\sin2\theta $, for $ 0\leq\theta\leq\frac{1}{2}\pi $. [2] (b) Sketch C and state the maximum distance of a poi…