Question

The equation $xy-a^2=a(x+y)$ represents

• A. A parabola
• B. Two perpendicular lines
• C. An ellipse
• D. Twp parallel straight lines

Answer 1

The correct option is B

Two perpendicular lines

Explanation for the correct answer:

Simplify the given equation.

An equation $xy-a^2=a(x+y)$ is given.

Simplify the given equation as follows:

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

Since the given equation $xy-a^2=a(x+y)$ is the pair of two lines and $y-a=0$. Which are perpendicular lines.

Hence, option $B$ is the correct answer.