OCR A Level: Further Pure 2 - Rational Graphs [June 2012 Q8]

Algebra Level pending

The curve \(C_1\) has equation \(y=\dfrac{p(x)}{q(x)}\), where \(p(x)\) and \(q(x)\) are polynomials of degree 2 and 1 respectively. The asymptotes of the curve are \(x=-2\) and \(y=\dfrac{1}{2}x+1\), and the curve passes through the point \(\left (-1, \dfrac{17}{2} \right )\).

\((\text{i})\) Express the equation of \(C_1\) in the form \(y=\dfrac{p(x)}{q(x)}\).

\((\text{ii})\) For the curve \(C_1\), find the range of values that \(y\) can take.

Another curve, \(C_2\), has equation \(y^2= \dfrac{p(x)}{q(x)}\), where \(p(x)\) and \(q(x)\) are the polynoimals found in part \((\text{i})\).

\((\text{iii})\) It is given that \(C_2\) intersects the line \(y=\dfrac{1}{2}x+1\) exactly once. Find the coordinates of the point of intersection.

If the coordinates of the point of intersection are \((m,n)\), input \(m+n\) as your answer.

There are 4 marks available for part (i), 4 marks for part (ii) and 4 marks for part (iii).
In total, this question is worth 16.7% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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