Polar coordinates and curves

The points A and B have polar coordinates  $\left(6,\ -\frac{\pi}{3}\right)\ and\ \left(8,\frac{\pi}{6}\right)\$  respectively.

The distance AB is

•  $2\sqrt{13}$  

•  $\sqrt{\left(100\ -\ 48\sqrt{3}\right)}$  

• 2

• 10

OQPR is a rhombus, where Q and R have polar coordiantes $\left(2,\frac{2\pi}{3}\right)\ and\ \left(2,0\right)$ respectively and O is the pole.  The polar coordinates of P are

•  $\left(2,\frac{\pi}{2}\right)$  

•  $\left(2,\frac{\pi}{3}\right)$  

•  $\left(2\sqrt{3},\frac{5\pi}{6}\right)$  

•  $\left(2\sqrt{3},\frac{\pi}{3}\right)$  

The polar coordinates of P are $\left(4,\frac{\pi}{4}\right)$  The pole,O, is the midpoint of the line PQ.

The Cartesian coordinates of Q are

•  $\left(-4\sqrt{2},-4\sqrt{2}\right)$  

•  $\left(-2\sqrt{2},-2\sqrt{2}\right)$  

•  $\left(-2\sqrt{3},-2\sqrt{3}\right)$  

•  $\left(-4,-\frac{3\pi}{4}\right)$  

A and B are the points of intersection of the line $r=\operatorname{cosec}\theta\ \$ and the circle  $r=4\cos\theta$  . O is the pole. 

The size of angle AOB, in radians,

 is

•  $\frac{\pi}{3}$  

•  $\frac{5\pi}{6}$  

•  $\frac{\pi}{4}$  

•  $\frac{5\pi}{12}$  

The radius of the circle with polar equation $r=6\cos\theta-2\sin\theta$ 

is 

• 4

• 6

•  $\sqrt{40}$  

•  $\sqrt{10}$  

A curve has polar equation $r^2\sin2\theta=1$  
The Cartesian equation of the curve is

•  $2\left(x^2+y^2\right)y=1$  

•  $xy=2$  

•  $2xy=1$  

•  $x^2+y^2=y$  

The circle with polar equation $r=\sqrt{3}$  intersects the curve with polar equation  $r=2\cos2\theta$  at the points P,Q,R and S.

The area of the quadrilateral PQRS is 

•  $6+2\sqrt{3}$  

•  $\frac{5\pi^2}{36}$  

•  $3\sqrt{3}$  

•  $3$  

The polar equation of this curve is

• $r=1+\cos2\theta$

• $r=\cos2\theta$

• $r=1+\cos\theta$

• $r=1-\cos\theta$

The polar equation of the curve is

• $r=\cos3\theta$

• $r=3\cos\theta$

• $r=3\sin\theta$

• $r=\sin3\theta$

The polar equation of the curve is

• $r=\cos3\theta$

• $r=\sin3\theta$

• $r=\sec3\theta$

• $r=\operatorname{cosec}3\theta$