Question

The value of $\lambda$ , for which the equation $x^2-y^2-x+\lambda y-2=0$ represents a pair of straight lines, are :

• A. $-3,1$
• B. $-1,1$
• C. $-3,3$
• D. $3,1$

Answer 1

Answer: (C)

We have, $x^2-y^2-x+\lambda y-2=0...(i)$
We know that,
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0...(ii)$
Now comparing Eqs. $(i)$ and $(ii)$, we get
$a=1,b=-1,c=-2,h=0,g=-1/2$,
$f=\lambda /2$
$\therefore$ Eq. $(ii)$ represents a pair of straight line, if
$abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$
$\therefore 2+0-\frac{{\lambda }^2}{4}+\frac{1}{4}=0$
$\Rightarrow \frac{{\lambda }^2}{4}=\frac{9}{4}$
$\Rightarrow \lambda =\pm 3$