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A chord overline(PQ) of the parabola ...

A chord `overline(PQ)` of the parabola `y^(2) =4ax` , subtends a right angle at the vertex , show that the mid point of `overline(PQ)` lies on the parabola, `y^(2) = 2a (x - 4a)` .

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Therefore, the mid point of the chord `overline(PQ)` lies on the parabola `y^(2) = 2a (x -4a)`
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