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\[<|\lambda -2|<1\]i.e., \[\lambda \in (1,2)\cup (2,3)\]
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