2026 IGCSE Additional Mathematics May/June 0606/13 Q12

2026 IGCSE Additional Mathematics May/June 0606/13 Q12

7 marks

A curve has equation \(y=e^{2a/x}\) where \(a\) is a positive constant.

  1. Find \(\dfrac{\mathrm dy}{\mathrm dx}\) in terms of \(a\).[2]
  2. The normal to the curve at the point where \(x=a\) passes through the origin.
    Find the value of \(a\).[5]

Solution:

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Answer:(a) \(-\dfrac{2a}{x^2}e^{2a/x}\) (b) \(a=\sqrt2\,e^2\)

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