Question

The differential equation of all circles whose centers are at the origin is:

• A. $\frac{dy}{dx}=\frac{y}{x}$
• B. $\frac{dy}{dx}=\frac{x}{y}$
• C. $\frac{dy}{dx}=-\frac{x}{y}$
• D. None of the above

Answer 1

The correct option is C $\frac{dy}{dx}=-\frac{x}{y}$

Now, general equation of a circle with center at origin is,

$x^2+y^2=r^2$

Differentiating w.r.t $x$, we get

$2x+2y\frac{dy}{dx}=0$

$⟹\frac{dy}{dx}=-\frac{x}{y}$

Hence, C is correct.