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)
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