Question

Show that the semi latus rectum of the parabola y2 = 4ax is a harmonic mean between the segment of any focal chord.

Answer 1

Equation of the given parabola is y2 = 4ax. 

Coordinates of focus = S(a, 0)

Let  and  be the end point of the focal chord of the given parabola.

∴ t1 t2 = – 1   ...(1)

Length of the semi latus rectum of the given parabola = 2a

Let SP and SQ be the segment of the focal chord.



Similarly,



⇒ 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.