Conic Sections: Challenge #6

Geometry Level 2

Sub-unit: Parabola

If normals at the end of a variable chord 'PQ' of the parabola \[ y^{2} = 4y +2x\] 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 \[ ax+by+c=0\]. Find the value of \[ a+b*c\].

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