Three normals are drawn from \(P(14,7)\) to the parabola \(y^2-16x-8y=0,\) A, B and C are conormal points, then area of \(\triangle ABG\) where \(G\) is centroid of \(\triangle ABC\) is \(\alpha\). Calculate \(\dfrac{45}{2}×\alpha\).

**Details and Assumptions**

- Conormal points are those points normal from which are concurrent. (Intersects at \(P\) in this case)

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