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Nikhil Chaudhari 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.

EXPERT ANSWER

Lalit Mehra , Meritnation Expert added an answer, on 18/1/12

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.

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.

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