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Question

The radius of the circle which touches the line x+y=0 at M(1,1) and cuts the circle x2+y2+6x4y+18=0 orthogonally, is
  1. 32
  2. 42
  3. 2
  4. 52


Solution

The correct option is D 52
Clearly, equation of the required circle is
(x+1)2+(y1)2+λ(x+y)=0x2+y2+(λ+2)x+(λ2)y+2=0     (1)


As circle (1) intersects the circle x2+y2+6x4y+18=0 orthogonally, so using orthogonality condition 2(g1g2+f1f2)=c1+c2, we get
2[(λ+22)32(λ22)]=18+2
(3λ+6)(2λ4)=20λ=10
Putting λ=10 in equation (1), we get
x2+y2+12x+8y+2=0.
Radius =62+422
           =50=52

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