For $l \in \mathbf{R}$, the equation $(2 l-3) x^2+2 l x y-y^2=0$ represents a pair of lines

• A

  only when $I=0$
• Correct answer
  B

  for all values of $/ \in R-(-3,1)$
• C

  for all values of $I \in(-3,1)$
• D

  for all values of $l \in R$

Solution

The equation $(2 l-3) x^2+2 l x y-y^2=0$ will represent a pair of real and distinct lines, if $l^2-(2 l-3)(-1)>0 \quad\left[\because h^2>a b\right]$ $\begin{array}{ll}\Rightarrow & l^2+2 l-3>0 \\ \Rightarrow & (l+3)(l-1)>0 \\ \therefore & l \in \mathbf{R}-(-3,1)\end{array}$

Hence, the correct answer is option: 'B'.