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Pearson Edexcel IAL Mathematics A2 FP2.7.1 Polar coordinates & sketching polar curves

Pearson Edexcel IAL Mathematics A2 FP2.7.1 Polar coordinates & sketching polar curves
Pearson Edexcel IAL Mathematics syllabusMathematics YMA01First assessment 2019

Practise reading and sketching polar curves, linking r and θ values to points, lines and parameters in bounded regions.

How this is tested

  • substitute a given θ into a polar curve and line equation to determine an exact parameter

Question 10(a)

[Maximum number: 2]
Figure 1

Figure 1

Figure 1 shows a sketch of the curve C with polar equation

r=1+cos⁡θ,0≤θ≤πr=1+\cos\theta,\qquad 0\le\theta\le\pi

and the line l with polar equation

r=ksec⁡θ,0≤θ<π2r=k\sec\theta,\qquad 0\le\theta<\frac{\pi}{2}

where k is a positive constant.

Given that
- C and l intersect at the point P
- OP=1+32OP=1+\frac{\sqrt3}{2}

determine the exact value of k.

The finite region R, shown shaded in Figure 1, is bounded by C, the initial line and l.