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# Find the differential equation of system of concentric circles with centre(1,2).

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

Toolbox:
• 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