The differential equation of the rectangular hyperbola $x y = c^{2}$ is
$y + x \frac{d y}{d x} = 0$
$\Rightarrow x \frac{d y}{d x} = - y$

Question

The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is (A) y (dy/dx) = x  (B) x (dy/dx) = - y  (C) x (dy/dx) = y  (D)  xdy + ydx = c

Tardigrade Admin · Accepted Answer

The differential equation of the rectangular hyperbola xy = c2 is y + x (dy/dx) = 0 ⇒ x (dy/dx) = - y

Q. The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

$y \frac{d y}{d x} = x$

$x \frac{d y}{d x} = - y$

$x \frac{d y}{d x} = y$

$x d y + y d x = c$

The differential equation of the rectangular hyperbola $x y = c^{2}$ is
$y + x \frac{d y}{d x} = 0$
$\Rightarrow x \frac{d y}{d x} = - y$

Q. The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

ydxdy​=x

xdxdy​=−y

xdxdy​=y

xdy+ydx=c

The differential equation of the rectangular hyperbola xy=c2 is y+xdxdy​=0 ⇒xdxdy​=−y

$y \frac{d y}{d x} = x$

$x \frac{d y}{d x} = - y$

$x \frac{d y}{d x} = y$

$x d y + y d x = c$

The differential equation of the rectangular hyperbola $x y = c^{2}$ is
$y + x \frac{d y}{d x} = 0$
$\Rightarrow x \frac{d y}{d x} = - y$