The differential equation of rectangular hyperbolas whose axes are asymptotes of the hyperbola $x^2-y^2=a^2$, is
Answer & explanation
Correct answer: option 2
The equation of the rectangular hyperbola whose axes are asymptotes of the hyperbola $x^2-y^2=a^2$ is
$x y=c^2$, where $c^2=a^2 / 2$
This is a one parameter family of curves. Differentiating with respect to $x$, we get
$x \frac{d y}{d x}+y=0 \Rightarrow x \frac{d y}{d x}=-y$