2026 ASRJC P1 Q4

2026 ASRJC P1 Q4

Junior College 2
6 marks

A curve \(C\) has equation \(x^2+3x-xy+3y-2=0\).

  1. For real values \(x\), use a non-graphical method to determine that \(y\) cannot lie between \(a\) and \(b\), where \(a\) and \(b\) are real constants to be determined.[3]
  2. Sketch the graph of \(C\), stating clearly the equations of any asymptotes and the coordinates of any turning points and axial intercepts.[3]

Solution:

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Answer:(i) \(a=1\), \(b=17\) (ii) asymptotes \(x=3\), \(y=x+6\); turning points \((-1,1)\), \((7,17)\); intercepts \((\frac{-3\pm\sqrt{17}}2,0)\), \((0,\frac23)\)

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