Parabola

Geometry Level 4

Akul draws a Tangent from any point (x1,y1)(x_{1},y_{1}) on the parabola y2y^{2}=4ax. He then draws tangents are from any point on this tangent to a circle centred at origin, having radius aa. Mayank obsserves that All the chords of contact pass through a fixed point (x2,y2)(x_{2},y_{2}).

Find k given that k(x1/x2)+(y1/y2)2k(x_{1}/x_{2})+(y_{1}/y_{2})^2=0

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