The curve $C$ has equation $y=\frac{{{x}^{2}}}{x-2}$. Find the equation(s) of the asymptote(s) of $C

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}}{x-2}$. Find the equation(s) of the asymptote(s) of $C$. [1] Sketch the curve $C$, labelling the equation(s) of its asymptote(s) and coordinates of any axial intercepts and turning points. [2] Hence find the range of values of $k$ for which the equation ${{x}^{2}}=k\left( {{x}^{2}}-4 \right)$ has no real roots.

Accepted Answer

(i) x = 2, y = x + 2; (ii) Graph with (0,0), (4,8); (iii) y₂ = k(x+2) passes through (−2, 0)

2013 YJC P1 Q12

2013 YJC P1 Q12

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