Co-Normal Parabolic Centroid

Geometry Level 5

Centroid of triangle formed by three Co-Normal points A(x1,y1),B(x2,y2) and C(x3,y3)A(x_1, y_1), B(x_2, y_2) \text{ and } C(x_3, y_3) on parabola y2=8xy^2 = 8x is G(4,0)G(4, 0). Two of the three points A,B and CA, B \text{ and } C lie above the x-axis\text{x-axis} or\underline{\text{or}} one of the point lies on x-axis. The normals drawn on parabola y2=8xy^2 = 8x at A,B and CA, B \text{ and } C are concurrent at M(h,k)M(h, k).

If h=ah = a and k>bk \gt b, enter answer as a2+b2a^2 + b^2.


All of my problems are original

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