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Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between the segments of any focal chord.
let the coordinates of end points for the focal chord drawn of the parabola be:P(at1^2,2at) and Q (at2^2, 2at2) respectively.SP = a+ at1^2 = > a (1+ t1^2)SQ = a(1 + t2^2)Now write SQ in terms of SP and then find1/SP + 1/SQ respectively.It would come as:1/a.
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