The angle between the lines $a b\left(x^2-y^2\right)+\left(a^2-b^2\right) x y=0$ is

The angle between the lines $a b\left(x^2-y^2\right)+\left(a^2-b^2\right) x y=0$ is
  1. $\frac{\pi}{2}$
  2. $\frac{\pi}{3}$
  3. $\frac{\pi}{4}$
  4. $\frac{\pi}{6}$

Solution

We have, $ \begin{aligned} & a b\left(x^2-y^2\right)+\left(a^2-b^2\right) x y=0 \\ & a b x^2+\left(a^2-b^2\right) x y-a b y^2=0 \end{aligned} $ Sum of the coefficient of $x^2$ and $y^2$ $ \text { i.e. } a b-a b=0 $ $\therefore \quad$ Lines are perpendicular to each other. $\therefore \quad$ Angle between lines $=\pi / 2$

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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