Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Show that the equation 
represents for different values of 
a system of circles passing through two fixed points 
and 
on the 
-axis, and also find the equation of that circle of the system the tangent to which at A and B meet on the line 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
S + λ L = 0
solving S = 0 & L = 0
put 
(x – 4) (x + 2) = 0
x = – 2 or 4
A ≡ (4, 0)
B ≡ (– 2, 0)
Equation of AB
Also equation of AB is x-axis i.e
0.x + 1.y + 0.c = 0...(2)
comparing (1) & (2)
Also , x + 2y + 5 = 0 ⇒ 1 – 
+ 5 = 0 ⇒ 6 = 
⇒ λ = 3
equation of circle is 
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