TS EAMCET · Maths · Pair of Lines
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 \(I=0\)
- B for all values of \(/ \in R-(-3,1)\)
- C for all values of \(I \in(-3,1)\)
- D for all values of \(l \in R\)
Answer & Solution
Correct Answer
(B) for all values of \(/ \in R-(-3,1)\)
Step-by-step Solution
Detailed explanation
The equation \((2 l-3) x^2+2 l x y-y^2=0\) will represent a pair of real and distinct lines, if \(l^2-(2 l-3)(-1)>0 \quad\left[\because h^2>a b\right]\) \(\begin{array}{ll}\Rightarrow & l^2+2 l-3>0 \\ \Rightarrow & (l+3)(l-1)>0 \\ \therefore & l \in \mathbf{R}-(-3,1)\end{array}\)
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