The curve $C$ has equation $y=\frac{a{{x}^{2}}+2}{x-1}$ where $x
e 1$ and $a$ is a non-zero constan

Question

The curve $C$ has equation $y=\frac{a{{x}^{2}}+2}{x-1}$ where $x
e 1$ and $a$ is a non-zero constant. Show that if the curve $C$ has no stationary points, then $-2 Sketch the curve for $a=1$, showing clearly the asymptotes and coordinates of any intersections with the coordinate axes. Verify that $y=k(x-1)+2$ passes through $(1,2)$ for all real values of $k$. By considering the equation of an appropriate line drawn on the same diagram with the curve $C$, find the range of values of $k$ for which the equation ${{x}^{2}}+2=k{{(x-1)}^{2}}+2(x-1)$ has no real roots.

Accepted Answer

$k\le 1$

2007 SAJC P1 Q7 [Modified]

2007 SAJC P1 Q7 [Modified]

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