Question

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

• A. $\mathrm{y}\frac{d\mathrm{y}}{d\mathrm{x}}=\mathrm{x}$
• B. $\mathrm{x}\frac{d\mathrm{y}}{d\mathrm{x}}=-\mathrm{y}$
• C. $\mathrm{x}\frac{d\mathrm{y}}{d\mathrm{x}}=\mathrm{y}$
• D. $\mathrm{x}\mathrm{dy}+\mathrm{y}\mathrm{dx}=\mathrm{c}$

Answer 1

The correct option is B

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

Explanation for the correct option:

Given, rectangular hyperbola where axes are asymptotes of hyperbola

The equation is $\mathrm{xy}={\mathrm{c}}^2$

On differentiating with respect to $x$,

$$\begin{gathered} y+x\left(\frac{dy}{dx}\right)=0 \\ \Rightarrow x\left(\frac{dy}{dx}\right)=-y \end{gathered}$$

Hence, the correct answer is option (B)