The ellipse $$\(E\)$$ has equation $$\[ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \]$$ The line $$\(l\)$$ is the normal to $$\(E\)$$ at the point $$\(P(5 \cos \theta, 3 \sin \theta)\)$$ where $$\(0< \theta< \frac{\pi}{2}\)$$ Using calculus, show that an equation for $$\(l\)$$ is $$\[ 5 x \sin \theta-3 y \cos \theta=16 \sin \theta \cos \theta \]$$ (4)

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