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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$x dy + y dx = c$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$x \frac{d y}{d x} = - y$

Explanation for the correct option:
Given, rectangular hyperbola where axes are asymptotes of hyperbola
The equation is $xy = c^{2}$
On differentiating with respect to $x$ ,
$y + x (\frac{d y}{d x}) = 0 \Rightarrow x (\frac{d y}{d x}) = - y$
Hence, the correct answer is option (B)

Suggest Corrections

Similar questions

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

Q. The vertices of

△ A B C

lie on a rectangular hyperbola such that the orthocentre of the triangle is

(3, 2)

and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. If two perpendicular tangents of the hyperbola intersect at the point

(1, 1)

,theb equation of the rectangular hyperbola is

Q. Assertion :The differential equation of the family of hyperbolas with asymptotes as the lines

x + y = 1

x - y = 1

given by

y \frac{d y}{d x} = x - 1

Reason: The eccentricity of rectangular hyperbola is

\sqrt{2}

Q. The vertices of

△ A B C

lie on a rectangular hyperbola such that the orthocentre of the triangle is

(3, 2)

and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. If two perpendicular tangents of the hyperbola intersect at the point

(1, 1)

,then combined equation of the asymptotes is

Which of the following statements are correct?

1. The particular kind of hyperbola in which the lengths of the transverse and conjugate axis are equal is called an equilateral hyperbola.

2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
3. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = 0$

4. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = - a^{2}$

Join BYJU'S Learning Program

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

The correct option is B xdydx=-yExplanation for the correct option:Given, rectangular hyperbola where axes are asymptotes of hyperbola The equation is xy=c2On differentiating with respect to x, y+xdydx=0⇒xdydx=-yHence, the correct answer is option (B)