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Question

One of the limiting points of the coaxial system of circles containing the circle x2+y26x6y+4=0 and x2+y22x4y+3=0 is:

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Solution

x2+y26x6y+4=0
x2+y22x4y+3=0
The equation of family of coaxial system of circles having 2 members is given by
(x2+y26x6y+4)+λ(4x2y+1)=0
x2+y22x(3+2λ)2y(3+λ)+(4+λ)=0 ……(1)
Centre of (1) (3+2λ,3+λ) & radius of (1)
(3+2λ)2+(3+λ)2(4+λ)=R
For limiting points radius
R=0
5λ2+17λ+14=0
λ=2,75
Limiting points are (1,1) & (15,85).

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