SAJC Graphing Techniques Tutorial Q1
The curve $C$ has equation
$y=\frac{2x-a}{2{{x}^{2}}-b}$,
where $a$ and $b$ are positive integers.
$C$ passes through point $\left( \frac{9}{2},0 \right)$ and the equation of an asymptote of $C$ is $x=3$.
(i)
Show that $a=9$ and $b=18$.
[2]
(ii)
Sketch $C$, stating clearly the equations of asymptotes, the $x-$coordinates of turning points and axial intercepts.
[4]
(iii)
Hence, giving your reasons, deduce the range of values of $h$ such that the graph of $\frac{{{\left( x-8 \right)}^{2}}}{{{h}^{2}}}+\frac{{{y}^{2}}}{100}=1$, where $h$ is a positive integer, intersects $C$ at exactly $6$ distinct points.
[3]
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