Question

The equation ${(x+y)}^2-(x^2+y^2)=0$ represents

• A. A circle
• B. Two lines
• C. Two parallel lines
• D. Two mutually perpendicular lines

Answer 1

The correct option is D

Two mutually perpendicular lines

Explanation for the correct answer:

Simplify the given equation.

An equation ${(x+y)}^2-(x^2+y^2)=0$ is given.

Simplify the given equation as follows:

$$\begin{gathered} {(x+y)}^2-(x^2+y^2)=0 \\ \Rightarrow x^2+y^2+2xy-x^2-y^2=0 \\ \Rightarrow 2xy=0 \\ \Rightarrow xy=0 \end{gathered}$$

So, the given line represents the pair of straight lines $x=0$ and $y=0$. Which are the equations of $x,y-$axes.

Therefore, the given equation ${(x+y)}^2-(x^2+y^2)=0$ represents the pair of two mutually perpendicular lines.

Hence, option $D$ is the correct .