The curve $C$ has equation given by $y=\frac{x-a+{{a}^{2}}}{a\left( x-a \right)}$, where \(

Question

The curve $C$ has equation given by $y=\frac{x-a+{{a}^{2}}}{a\left( x-a \right)}$, where $a$ is a negative constant. Write down the equations of the asymptotes of $C$.[2] Sketch the graph of $C$, labelling clearly the asymptotes and axial intercepts.[2] Deduce the range of values of $k$ for which the equation $\frac{x-a+{{a}^{2}}}{a\left( x-a \right)}=k$ has one negative real root.[2] State the range of values of $x$ for which the curve is concave downwards.[1]

Accepted Answer

(i) ${y=\frac{1}{a}\,,\, x=a}$ (iii) ${k\frac{1}{a}}$ (iv) ${x>a}$

2012 NJC Promo Q11

2012 NJC Promo Q11

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