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A variable chord PQ of the parabola y^(2...

A variable chord PQ of the parabola `y^(2)=4ax` is drawn parallel to the line y = x if the parameter of the points P and Q on the parabola be `t_(1)andt_(2)` respectively and then prove that `t_(1)+t_(2)=2`. Also show that the locus of the point of intersection of the normals at P and Q is 2x - y = 12a.

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