# 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.

###### This is part of the set OCR A Level Problems.
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