2025 NJC P1 Q5
2025 NJC P1 Q5
8 marks
The curve \(C\) has equation \[y = \frac{2x^2 + kx + 8}{x + p},\]where \(k\) and \(p\) are constants. It is given that \(C\) has a vertical asymptote \(x = 2\) and a stationary point at \(x = -4\).
- Find the equation of the oblique asymptote of \(C\).[5]
- Sketch \(C\), clearly labelling the equations of asymptotes and the coordinates of stationary points.[3]
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Answer:(i) \(y=2x+32\) (ii) Asymptotes \(x=2\) and \(y=2x+32\); stationary maximum \((-4,12)\) and minimum \((8,60)\)
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