Published by:
CGP EDU Academic Team
Published on: August 14, 2026
AB, AC are tangents to a parabola y 2 = 4ax. If l 1 , , l 3 are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then -
Text Solution
Verified by ExpertsThe correct answer is:
B
Let the coordinates of B and C be (at 1 2 , 2at 1 ) and (at 2 2 , 2at 2 ) respectively. Then, the coordinates of A are (at 1 t 2 , a(t 1 + t 2 )).
The equation of any tangent to y 2 = 4ax is
ty = x + at 2 ∴ l 1 = 
,
l 2 = 
and l 3 = 
Clearly, l 2 l 3 = l 1
2 . Therefore, l 2 , l 1 , l 3 are in G.P.
Hence is the correct answer.
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