Question

If the lines $x^2+(2+k)xy-4y^2=0$ are equally inclined to the coordinate axes then $K$ =

• A. $-1$
• B. $-2$
• C. $-3$
• D. $-4$

Answer 1

The correct option is B $-2$

$x^2+(2+k)xy-4y^2=0$.

dividing by $x^2.$

$\Rightarrow 1+(2+k)\frac{y}{x}-4\frac{y^2}{x^2}=0$

using $\frac{y}{x}=m$

$\Rightarrow 1+(2+k)m-4m^2=0$

$\Rightarrow 4m^2-(2+k)m-1=0$

This equation will give the slope of both the lines as lines are equally inclined.

$\Rightarrow$ slope of lines will be equal and of opposite sign.

$\Rightarrow m_1+m_2=0$

$\Rightarrow$ Sum of roots $=\frac{-(-(2+k\left)\right)}{4}=0$

$\Rightarrow 2+k=0$

$\Rightarrow k=-2$