Question

The equation of the lines represented by the equation $ab(x^2-y^2)+(a^2-b^2)xy=0$are

• A. $ax–by=0,bx+ay=0$
• B. $ax–by=0,bx–ay=0$
• C. $ax+by=0,bx+ay=0$
• D. $ax+by=0,bx–ay=0$

Answer 1

The correct option is A

$ax–by=0,bx+ay=0$

Explanation of the correct option:

Given: $ab(x^2-y^2)+(a^2-b^2)xy=0$

$\Rightarrow$ $ab{x}^2-ab{y}^2+a^{2}xy-b^{2}xy=0$

$\Rightarrow$ $ax(bx+ay)-by(ay+bx)=0$

$\Rightarrow$ $\left(bx+ay\right)(ax-by)=0$

Separate equations are,

$bx+ay=0$

$ax-by=0$

Hence Option $\left(\mathrm{A}\right)$ is the correct answer.