Question

The differential equation of 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

Answer: (B)

Given that centre of circle is $(1,2)$.
Let radius of circle is $a$.
We know that equation of circle is
$(x-h{)}^2+(y-k{)}^2=r^2$
where, $h=1,k=2$, and $r=a$
$\therefore (x-1{)}^2+(y-2{)}^2=a^2$
On differentiating, we get
$2\left(x-1\right)+2\left(y-2\right)\frac{dy}{dx}=0$
$\Rightarrow \left(x-1\right)+\left(y-2\right)\frac{dy}{dx}=0$
which is required differential equation.