Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The squared length of the intercept made by the line x = h on the pair of tangents drawn from the origin to the circle x 2 + y 2 + 2gx + 2fy + c = 0 is
A
(g 2 + f 2 – c)
B
(g 2 + f 2 – c)
C
(g 2 + f 2 – c)
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Equation of pair of tangents from (0, 0) is
SS ′ = T 2 ⇒ (x 2 + y 2 + 2gx + 2fy + c)
c = (gx + fy + c) 2 ... (i)
The intersection points of the above pair with x = h is given by
(gh + fy + c) 2 = (h 2 + y 2 + 2gh + 2fy + c) c
⇒ (f 2 – c) y 2 + 2fghy + h 2 (g 2 – c) = 0
If its roots are 
and 
, then length of intercept
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