A) 3
B) 2
C) 1
D) 4
Correct Answer: B
Solution :
Equation of required circle is \[{{x}^{2}}+{{y}^{2}}+\frac{2(2\lambda -1)}{\lambda +1}\,x+\frac{2(2-\lambda )}{1+\lambda }\,y-\frac{(1+5\lambda )}{1+\lambda }=0\] Now, using condition of orthogonality, we get \[-4=\frac{1+5\lambda }{1+\lambda }\,\Rightarrow \,\lambda =\frac{-5}{9}\] So, the equation of circle is \[{{x}^{2}}+{{y}^{2}}\,-\frac{19}{2}\,x+\,\frac{23}{2}\,y+4=0\]
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