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

The family of concentric circles with

centre (1,2) and radius $a$ is given
by
${(x - 1)^2} + {(y - 2)^2} = {a^2}$

$\Rightarrow$ ${x^2} + 1 - 2x + {y^2} + 4 - 4y = {a^2}$

$\Rightarrow$ ${x^2} + {y^2} - 2x - 4y + 5 = {a^2}$

……..(i)
On differentiating Eq. (i) w.r.t. $x$,

we get
$2x + 2y\frac{{dy}}{{dx}} - 2 - 4\frac{{dy}}{{dx}} = 0$

$\Rightarrow$ $(2y - 4)\frac{{dy}}{{dx}} + 2x - 2 = 0$

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

LONG ANSWER QUESTIONS