9231 P11 - Jun 2019 - Q10 - 12 marks
5824
10 The curves \(C_{1}\) and \(C_{2}\) have equations
\(y=\frac{a x}{x+5} \quad \text { and } \quad y=\frac{x^{2}+(a+10) x+5 a+26}{x+5}\)
respectively, where \(a\) is a constant and \(a>2\).
(i) Find the equations of the asymptotes of \(C_{1}\).
(ii) Find the equation of the oblique asymptote of \(C_{2}\).
(iii) Show that \(C_{1}\) and \(C_{2}\) do not intersect.
(iv) Find the coordinates of the stationary points of \(C_{2}\).
(v) Sketch \(C_{1}\) and \(C_{2}\) on a single diagram. [You do not need to calculate the coordinates of any points where \(C_{2}\) crosses the axes.]
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