Question

Consider a general equation of degree $2$, as $\lambda x^2-10xy+12y^2+5x-16y-3=0$

The values of $\lambda$ for which the equation represents a pair of straight lines is

• A. $1$
• B. $2$
• C. $\frac{3}{2}$
• D. $3$

Answer 1

Answer: (B)

$2$

From given, we have,

$a=\lambda ,h=-5,b=12,g=\frac{5}{2},f=-8,c=-3$

$\lambda \left(12\right)(-3)+2(-8)\left(\frac{5}{2}\right)(-5)-\lambda \left(64\right)-\left(\frac{25}{4}\right)12+3\times 25=0$

$-36\lambda +200-64\lambda -75+75=0$

$\Rightarrow 100\lambda =200$

$\therefore \lambda =2$