$\begin{array}{1 1}(A)\;(x-1)+(y-2)\large\frac{dy}{dx}=0 \\(B)\;(x-1)-(y-2)\large\frac{dy}{dx}=0 \\ (C)\;(x+1)+(y-2)\large\frac{dy}{dx}=0 \\ (D)\;(x+1)-(y+2)\large\frac{dy}{dx}=0\end{array} $

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- Equation of family of circles, with center $(h,k)$ and radius $a$ is $(x-h)^2+(y-k)^2=a^2$
- If an equation has $'n'$ arbitrary constants, then it differentail equation is of $n^{th}$ order

Given : Concentric circles with center(1,2)

The equation of concentric circles with centre(1,2) is

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

Now let us differentiate w.r.t x

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

Dividing throughout by 2,

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

This is the required equation

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