The curve $C$ has equation $y=\frac{{{x}^{2}}+ax+10}{x-b}$. The asymptotes of $C$ are $x=3$ and $y=x

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}+ax+10}{x-b}$. The asymptotes of $C$ are $x=3$ and $y=x-2$. Find the values of $a$ and $b$. [2] Sketch $C$, showing its asymptotes and the coordinates of axial intercept and turning points. [3] Deduce the range of values of $k$, where $k$ is a positive real constant such that the equation ${{\left( x-1 \right)}^{2}}+{{\left( \frac{{{x}^{2}}+ax+10}{x-b} \right)}^{2}}={{k}^{2}}$ has at least one real root. [2]

Accepted Answer

(i) $a=-5,b=3$; (iii) $k\ge3$

2018 MJC Promo Q3

2018 MJC Promo Q3

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