Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the focus of a parabola divides a focal chord of the parabola in segments of length 3 and 2, the length of the latus rectum of the parabola is-
Text Solution
Verified by ExpertsThe correct answer is:
D
Let y 2 = 4ax be the equation of the parabola, then the focus is S(a, 0). Let P(at 1 2 , 2at 1 ) and Q(at 2 2 , at 2 ) be vertices of a focal chord of the parabola, then t 1 t 2 = –1. Let SP = 3, SQ = 2
SP = 
= a(1 + t 1 2 ) = 3 (i)
and SQ = a 
= 2
From (i) and (ii) we get t 1 2 = 3/2 and a = 6/5
Hence the length of the latus rectum = 24/5.
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