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$
$∴ (x - 1 )^2 + ( y - 2 )^2 = a^2$
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.