Q77 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics
The quadrilateral formed by the pairs of line $x y+x+y+1=0, x y+3 x+3 y+9=0$ is
- AParallelogram
- BRhombus
- CRectangle
- Correct answerDSquare
Solution
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.
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.
Hence, the correct answer is option: 'D'.