The ellipse $$\(E\)$$ has equation $$\[ \frac{x^{2}}{49}+\frac{y^{2}}{b^{2}}=1 \]$$ where $$\(b\)$$ is a constant and $$\(0< b< 7\)$$ The eccentricity of the ellipse is $$\(e\)$$ Given that - the point $$\(P(x, y)\)$$ lies on $$\(E\)$$ where $$\(x> 0\)$$ - the point $$\(S\)$$ is the focus of $$\(E\)$$ on the positive $$\(x\)$$-axis - the line $$\(l\)$$ is the directrix of $$\(E\)$$ which crosses the positive $$\(x\)$$-axis - the point $$\(M\)$$ lies on $$\(l\)$$ such that the line through $$\(P\)$$ and $$\(M\)$$ is parallel to the $$\(x\)$$-axis (b) determine an expression for (i) $$\(P S^{2}\)$$ in terms of $$\(e, x\)$$ and $$\(y\)$$ (ii) $$\(P M^{2}\)$$ in terms of $$\(e\)$$ and $$\(x\)$$ (2)

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