Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If a variable line, 3x + 4y – λ = 0 is such that the two circles x 2 + y 2 – 2x –2y + 1 = 0 and
x 2 + y 2 –18x –2y +78 = 0 are on its opposite sides, then the set of all values of λ is the interval:
Text Solution
Verified by ExpertsThe correct answer is:
B
3x + 4y – λ = 0
(7 – λ )(31 – λ ) < 0 {since centres lie opposite side}
(7 – λ )(31 – λ ) < 0
λ ∈ (7, 31) ……
& 
λ ≤ 2 or λ ≥ 12 …. & λ ≤ 21 or λ ≥ 41 ….
∩ ∩
λ ∈ [12, 21]
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