Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The line l x + my = 1 intersects the circle x 2 + y 2 = a 2 at points A, B, if AB subtends 45° at the origin, then a 2 ( l 2 + m 2 ) -
A
4 ± 2 
B
4 ±2 
C
2 
D
4 – 
Text Solution
Verified by ExpertsThe correct answer is:
A
Homogenise the equation of the circle with the help of the equation of the line
x 2 + y 2 = a 2 (1) 2 = x 2 + y 2 = a 2 ( l x + my) 2
⇒ (a 2 l 2 – 1) x 2 + 2 l ma 2 xy + (a 2 m 2 – 1) y 2 = 0
∴ tan 45 0 = 
Squaring, we get 1 = 
⇒ a 4 ( l 2 + m 2 ) – 8a 2 ( l 2 + m 2 ) + 8 = 0
∴ l 2 + m 2 = 
a 2 ( l 2 + m 2 ) = 4 ± 2 
.
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