300 followers problem! Conics!

Geometry Level 5

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)