Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If a circle C passing through the point (4,0) touches the circle x 2 + y 2 + 4x – 6y = 12 externally at the point (1, –1), then the radius of C is:
A
2 
B
C
4
D
5
Text Solution
Verified by ExpertsThe correct answer is:
D
Tangent at (1,–1) is x(a) + y(–1) + 2 (x + 1) – 3 (y – 1) – 12 = 0
⇒ 3x –4y = 7
Required circle is
(x – 1) 2 + (y + 1) 2 + λ (3x – 4y–7) = 0
It pass through (4,0)
⇒ 9 + 1 + λ (12 – 7) = 0 ⇒ λ = – 2 ⇒ required circle is x 2 + y 2 – 8x + 10y + 16 = 0
⇒ Radius = 
= 5
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