Question 9 - A-Level Maths

The line $L$ has polar equation $$r = \frac { 7 } { 4 } \sec \theta \quad \left( - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } \right)$$ Show that $L$ is perpendicular to the initial line.
9
The curve $C$ has polar equation $$r = 3 + \cos \theta \quad ( - \pi < \theta \leq \pi )$$ Find the polar coordinates of the points of intersection of $L$ and $C$ Fully justify your answer.
9
The region $R$ is the set of points such that
and $$r > \frac { 7 } { 4 } \sec \theta$$ Find the exact area of $R$ $$r < 3 + \cos \theta$$ Find the exact area of $R$
[0pt] [7 marks]