Prove that in a parabola, a circle of an...

Prove that in a parabola, a circle of any focal radii of a point `P(at^2,2at)` as diameter touches the tangent at the vertex and intercepts a chord of length `a[(1+t^2)]^0.5` on a normal at the point P.

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Let y^(2)=4ax be a parabola and PQ be a focal chord of parabola.Let T be the point of intersection of tangents at P and Q. Then