Question

The equation $x^2+(\lambda +\mu )xy+\lambda \mu y^2+x+\mu y=0$ represents two parallel straight lines if

• A. $\lambda +\mu =0$
• B. $\lambda =4\mu$
• C. $\lambda =\mu$
• D. none of these

Answer 1

The correct option is C $\lambda =\mu$

Let take two parrallel lines are $ax+by+c_1=0$ and $ax+by+c_2=0$

So, the combined equation is

$a^2{x}^2+2abxy+b^2{y}^2+ax(c_1+c_2)+by(c_1+c_2)+c_1{c}_2=0$ and compare with given equation

By comparison

$\lambda +\mu =2ab,\lambda \mu =b^2$

By solving, get $(\lambda -\mu {)}^2=0$

Hence,$\lambda =\mu$