2025 ASRJC Promo Q2

2025 ASRJC Promo Q2

Junior College 1
6 marks

A curve has equation \(2x^2+3xy+y^2=12\).

  1. Find the gradient of the normal to the curve at the point \((1,2)\). Hence, determine the equation of the normal at this point.[4]
  2. Find the exact area of the triangle enclosed by the normal obtained in part (a) and the axes.[2]

Solution:

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Answer:(a) gradient \(\dfrac7{10}\), normal \(y=\dfrac7{10}x+\dfrac{13}{10}\) (b) \(\dfrac{169}{140}\)

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