A) \[(0,\,\,1]\]
B) \[(-1,\,\,2)\]
C) \[(2,\,\,3)\]
D) \[(-1,\,\,0)\]
Correct Answer: C
Solution :
\[{{\left( x-\frac{1}{5} \right)}^{2}}+{{\left( y-\frac{2}{5} \right)}^{2}}=({{\lambda }^{2}}-4\lambda +4){{\left( \frac{3x+4y-1}{5} \right)}^{2}}\]\[i.e.,\,\,\sqrt{{{\left( x-\frac{1}{5} \right)}^{2}}+{{\left( y-\frac{2}{5} \right)}^{2}}}=|\lambda -2|\left| \frac{3x+4y-1}{\sqrt{5}} \right|\]is an ellipse. If\[0<|\lambda -2|\,\,<1\,\,i.e.,\,\,\lambda \in (1,\,\,2)\cup (2,\,\,3)\]
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