Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between the segments of any focal chord.

Question

Vikas TU · Answer

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 find 1/SP + 1/SQ respectively. It would come as: 1/a.

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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.

Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between the segments of any focal chord.

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