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From a variable point P(t^(2),2t)(1letle...

From a variable point `P(t^(2),2t)(1letle3)` on the parabola `y^(2)=4x`, perpendicular PM is drawn to the tangent at the vertex of the parabola. Now from the mid point Q of PM perpendicular QL is drawn to the focal chord of the parabola through P. If maximum length of `QLltk`, where `kinN` then find the value of k.

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Knowledge Check

  • Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in

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    `(1)/(2)`
    B
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    C
    `(3)/(2)`
    D
    2

  • If the tangent at the extrenities of a chord PQ of a parabola intersect at T, then the distances of the focus of the parabola from the points P.T. Q are in

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    A.P
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