The ellipse $$\(E\)$$ has equation $$\[ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \]$$ The line $$\(l\)$$ is the normal to $$\(E\)$$ at the point $$\(P(5 \cos \theta, 3 \sin \theta)\)$$ where $$\(0< \theta< \frac{\pi}{2}\)$$ Given that - $$\(\quad l\)$$ intersects the $$\(y\)$$-axis at the point $$\(Q\)$$ - the midpoint of the line segment $$\(P Q\)$$ is $$\(M\)$$ (b) determine the exact maximum area of triangle $$\(O M P\)$$ as $$\(\theta\)$$ varies, where $$\(O\)$$ is the origin. You must justify your answer. (5)

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