Published by:
CGP EDU Academic Team
Published on: August 14, 2026
A circle passing through the point {2, 2( 
– 1)} touches the pair of lines x 2 – y 2 – 4x + 4 = 0. The centre of the circle is -
A
(2, 2 
) & (2, 6 
– 8)
) & (2, 6 – 8)
B
(2, 5 
) & (2, 7 
)
) & (2, 7 )
C
(2, 5 
– 1) & (2, –3)
– 1) & (2, –3)
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
The equation of the pair of lines is
(x – 2) 2 – y 2 = 0
i.e. (x – 2) = ± y
i.e. x – y = 2 and x + y = 2
The centre of the circle touching the above lines must lie on the angular bisectors of the above lines. Hence, C ≡ (2, k) (see figure)
Thus we have CM = CP
i.e. 
= 2( 
– 1) – k
i.e. ± 
= 2( 
– 1) – k
i.e. k 
= 2( 
– 1)
gives k = 
= 
, 
( 
– 1) 2
= 
, 
– 8.
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