Challenging +1.2 This is a Further Maths FP2 polar coordinates question requiring students to find where dr/dθ = 0 (for tangent parallel to initial line), then substitute back to find r. It involves differentiation of a trigonometric expression and solving a standard equation, but the multi-step nature and the polar geometry concept make it moderately challenging beyond typical A-level, though still a fairly standard FP2 exercise.
The curve \(C\) has polar equation
$$r = 1 + 2 \cos \theta, \quad 0 \leq \theta \leq \frac{\pi}{2}.$$
At the point \(P\) on \(C\), the tangent to \(C\) is parallel to the initial line.
Given that \(O\) is the pole, find the exact length of the line \(OP\). [7]
The curve $C$ has polar equation
$$r = 1 + 2 \cos \theta, \quad 0 \leq \theta \leq \frac{\pi}{2}.$$
At the point $P$ on $C$, the tangent to $C$ is parallel to the initial line.
Given that $O$ is the pole, find the exact length of the line $OP$. [7]
\hfill \mbox{\textit{Edexcel FP2 Q2 [7]}}