Question

The differential equation of system of concentric circles with centres $(1,2)$ is

• A. $\frac{dy}{dx}=\frac{x-1}{x-2}$
• B. $\frac{dy}{dx}=\frac{x-1}{2-x}$
• C. $\frac{dy}{dx}=\frac{x-1}{2-y}$
• D. $\frac{dy}{dx}=\frac{x-1}{y-2}$

Answer 1

The correct option is C $\frac{dy}{dx}=\frac{x-1}{2-y}$

General equation of concentric circles with centres $(1,2)$ is

$(x-1{)}^2+(y-2{)}^2=a^2$ where $a$ is radius of the concentric circles.

Differentiating it, we get

$2(x-1)+2(y-2)\frac{dy}{dx}=0$

$\Rightarrow \frac{dy}{dx}=-\frac{x-1}{y-2}=\frac{x-1}{2-y}$

Hence, C is the correct option.