- (a) Sketch the polar curve \(C\), with equation
$$r = 3 + \sqrt { 5 } \cos \theta \quad 0 \leqslant \theta \leqslant 2 \pi$$
On your sketch clearly label the pole, the initial line and the value of \(r\) at the point where the curve intersects the initial line.
The tangent to \(C\) at the point \(A\), where \(0 < \theta < \frac { \pi } { 2 }\), is parallel to the initial line.
(b) Use calculus to show that at \(A\)
$$\cos \theta = \frac { 1 } { \sqrt { 5 } }$$
(c) Hence determine the value of \(r\) at \(A\).