Figure 4 shows a sketch of the closed curve with equation $$\[ (x+y)^{3}+10 y^{2}=108 x \]$$ (a) Show that $$\[ \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{108-3(x+y)^{2}}{20 y+3(x+y)^{2}} \]$$ (5) The curve is used to model the shape of a cycle track with both $$\(x\)$$ and $$\(y\)$$ measured in $$\(\mathrm{km}\)$$. The points $$\(P\)$$ and $$\(Q\)$$ represent points that are furthest north and furthest south of the origin $$\(O\)$$, as shown in Figure 4. Using the result given in part (a), (b) find how far the point $$\(Q\)$$ is south of $$\(O\)$$. Give your answer to the nearest $$\(100 \mathrm{~m}\)$$. (4)

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