Conic Sections: Challenge #6

Geometry Level 3

Sub-unit: Parabola

If normals at the end of a variable chord 'PQ' of the parabola y 2 = 4 y + 2 x y^{2} = 4y +2x are perpendicular to each other then the locus of point of intersection of tangents at 'P' and 'Q' is a straight line which has the equation a x + b y + c = 0 ax+by+c=0 . Find the value of a + b c a+b*c .


The answer is 2.

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