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CGP EDU Academic Team
Published on: August 14, 2026
If 4 l 2 – 5m 2 + 6 l + 1 = 0 and the line l x + my + 1 = 0 touches a fixed circle, then -
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b)
Let the circle be (x – h) 2 + (y – k) 2 = r 2
then r = 
( l m + my + 1 = 0 is tangent)
⇒ r 2 ( l 2 + m 2 ) = ( l h + mk + 1) 2
l 2 (h 2 – r 2 ) + m 2 (k 2 – r 2 ) + 2 l mhk + 2 l h + 2mk + 1 = 0 … (1)
also 4 l 2 – 5m 2 + 6 l + 1 = 0 … (2)
Comparing the coefficients of similar terms
h 2 – r 2 = 4, k 2 – r 2 = –5, hk = 0, 2h = 6, 2k = 0
∴ k = 0, h = 3 and 9 – r 2 = 4,
∴ r 2 = 5
Centre (3, 0) and radius = 
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