A variable \( \triangle \mathrm{ABC} \) in the xy plane has its ort...

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A variable \( \triangle \mathrm{ABC} \) in the xy plane has its orthocentre at vertex 'B', a fixed vertex 'A' at the origin and the
\( \mathrm{P} \) third vertex ' \( C \) ' restricted to lie on the parabola \( y=1+\frac{7 x^{2}}{36} \). The point \( B \) starts at the point \( (0,1) \) at time

W \( \mathrm{t}=0 \) and moves upward along the \( \mathrm{y} \) axis at a constant velocity of \( 2 \mathrm{~cm} / \mathrm{sec} \). How fast is the area of the triangle increasing when \( \mathrm{t}=\frac{7}{2} \mathrm{sec} \).
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