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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.

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
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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