The quadrilateral formed by the pairs of line $x y+x+y+1=0, x y+3 x+3 y+9=0$ is

Question

Aicharya · Accepted Answer

Given pair of lines $ \begin{array}{rlrl} x y+x+y+1 & =0 \\ x(y+1)+(y+1) & =0 \\ & & (y+1)(x+1) & =0 \\ \Rightarrow \quad & \quad x & =-1 \text { or } y=-1 \end{array} $

and second pair of line $ \begin{aligned} x y+3 x+3 y+9 & =0 \\ x(y+3)+3(y+3) & =0 \\ (x+3)(y+3) & =0 \\ x=-3 \text { or } y & =-3 \end{aligned} $ $\therefore$ Quadrilateral so formed by above lines is a square Hence, option (4) is correct

The quadrilateral formed by the pairs of line $x y+x+y+1=0, x y+3 x+3 y+9=0$ is

Solution