The curve $C$ has the equation of $y=\frac{{{x}^{2}}-8}{x-2}$. Show that $C$ has no stati

Question

The curve $C$ has the equation of $y=\frac{{{x}^{2}}-8}{x-2}$. Show that $C$ has no stationary points. Sketch the curve $C$, showing clearly the asymptotes and coordinates of any intersections with the coordinate axes. 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 the equation ${{x}^{2}}-8=k{{(x-2)}^{2}}+4(x-2)$ to have no real roots.

Accepted Answer

$k \geq 1$

2013 ACJC J1 MYE Q4

2013 ACJC J1 MYE Q4

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