Question

Pair of straight lines perpendicular to each other represented by

• A. $2x^2=2y(2x+y)$
• B. $x^2+y^2+3=0$
• C. $2x^2=y(2x+y)$
• D. $x^2=2(x–y)$

Answer 1

The correct option is A

$2x^2=2y(2x+y)$

Explanation for the correct option:

Option (A): $2x^2=2y(2x+y)$

If a pair of straight lines are perpendicular to each other,

then the coefficient of $x^2$ + coefficient of$y^2$ = 0

Here,

$$\begin{gathered} 2x^2=2y(2x+y) \\ 2x^2-4xy–2y^2=0 \end{gathered}$$

coefficient of x² + coefficient of y² = 0

$2-2=0$

Therefore, the given pair of straight lines are perpendicular to each other.

Explanation for the incorrect options:

Option (B):$x^2+y^2+3=0$

Here, $1+1=2$

Therefore, the given pair of straight lines are not perpendicular to each other.

Option (C):$2x^2=y(2x+y)$

Here, $2-1=1$

Therefore, the given pair of straight lines are not perpendicular to each other.

Option (D):$x^2=2(x–y)$

Here, $1-0=1$

Therefore, the given pair of straight lines are not perpendicular to each other.

Hence, option (A) is the correct answer.