300 followers problem! Conics!

Geometry Level 5

Three normals are drawn from P(14,7)P(14,7) to the parabola y216x8y=0,y^2-16x-8y=0, A, B and C are conormal points, then area of ABG\triangle ABG where GG is centroid of ABC\triangle ABC is α\alpha. Calculate 452×α\dfrac{45}{2}×\alpha.

Details and Assumptions

  • Conormal points are those points normal from which are concurrent. (Intersects at PP in this case)
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