Show that the semi latus rectum of the parabola y2 = 4ax is a harmonic mean between the segment of any focal chord.
Equation of the given parabola is y 2 = 4ax.
Coordinates of focus = S(a, 0)
Let and be the end point of the focal chord of the given parabola.
∴ t 1 t 2 = – 1 ...(1)
Length of the semi latus rectum of the given parabola = 2a
Let SP and SQ be the segment of the focal chord.
⇒ SP, 2a and SQ are in H.P.
Thus, the semi latus rectum of the given parabola is the harmonic mean between the segment of the local chord.
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