A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
Points of intersection with co-ordinate axes are \[\left( -\frac{1}{\lambda },\ 0 \right)\text{ },\text{ }\ (0,\ 1)\] and \[(-3,\ 0),\ \left( 0,\ \frac{3}{2} \right)\]. Equation of circle through (0, 1), (?3, 0) and \[\left( 0,\ \frac{3}{2} \right)\] is \[{{x}^{2}}+{{y}^{2}}+\frac{7x}{2}-\frac{5y}{2}+\frac{3}{2}=0\]. It passes through \[\left( \frac{-1}{\lambda },\ 0 \right)\] \[\Rightarrow \frac{1}{{{\lambda }^{2}}}-\frac{7}{2\lambda }+\frac{3}{2}=0\Rightarrow 3{{\lambda }^{2}}-7\lambda +2=0\] \[\Rightarrow \lambda =\frac{7\pm \sqrt{49-24}}{6}=\frac{7\pm 5}{6}=2,\ \frac{1}{3}\].
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