Question

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

• A. $(x–2)+(y–1)\frac{dy}{dx}=0$
• B. $(x–1)+(y–2)\frac{dy}{dx}=0$
• C. $(x+1)\frac{dy}{dx}+(y–2)=0$
• D. $(x+2)\frac{dy}{dx}+(y–1)=0$

Answer 1

The correct option is B

$(x–1)+(y–2)\frac{dy}{dx}=0$

Explanation for the correct option:

Given are the concentric circles with centre $(1,2)$

Equation of circle with centre $(a,b)$ and radius $r$ is

$$\begin{gathered} {\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2 \\ {\left(x-1\right)}^2+{\left(y-2\right)}^2=r^2 \end{gathered}$$

On Diffenrentiating above equation with respect to $x$ we get,

$$\begin{gathered} 2\left(x-1\right)+2\left(y-2\right)\frac{dy}{dx}=0 \\ \left(y-2\right)\frac{dy}{dx}+\left(x-1\right)=0 \end{gathered}$$

Hence, the correct answer is option (B)