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from ST. PAUL'S HR.SEC.SCHOOL, asked a question
Subject: Math , asked on 18/1/12

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.

âˆ´ t 1 t 2 = â€“ 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,

â‡’ 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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