2024 IGCSE Additional Mathematics February/March 0606/22 Q7

2024 IGCSE Additional Mathematics February/March 0606/22 Q7

7 marks
  1. The curves \(4x^2-3y^2+xy=24\) and \(y=\dfrac2x\) intersect at the points \(P\) and \(Q\). Find the coordinates of \(P\) and \(Q\).[5]
  2. Find the length of \(PQ\). Give your answer in the form \(a\sqrt b\), where \(a\) is rational and \(b\) is the smallest possible integer.[2]

Solution:

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Answer:(a) \(\left(\sqrt6,\dfrac{\sqrt6}3\right)\), \(\left(-\sqrt6,-\dfrac{\sqrt6}3\right)\). (b) \(\dfrac{4\sqrt{15}}3\).

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