A) \[-\frac{1}{6}\]
B) \[\frac{1}{6}\]
C) \[-\frac{1}{4}\]
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
[c] \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}-3x+ky-5=0.\] \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}-3x-\frac{y}{4}-\frac{9}{4}=0.\] \[{{S}_{1}}\text{ }\!\!\And\!\!\text{ }{{S}_{2}}\]be concentric i.e. they have the common centre Centre of \[{{S}_{1}}\equiv \left( \frac{3}{2},\frac{-k}{2} \right),\]Centre of \[{{S}_{2}}\equiv \left( \frac{3}{2},\frac{1}{8} \right),\] \[\Rightarrow \frac{-k}{2}=\frac{1}{8}\Rightarrow k=\frac{-1}{4}\] Hence, option [c] is correct.
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