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

Options

A. `(dy)/(dx)=(x-1)/(x-2)`
B. `(dy)/(dx)=(x-1)/(2-x)`
C. `(dy)/(dx)=(1-x)/(2-y)`
D. `(dy)/(dx)=(1-x)/(y-2)`

Answer

d

Explanation

The equation of family of circles (cooncentric) with centre (1,2) is
` (x-1)^(2) + (y-2)^(2) = r^(2)`
(where , r is parameter ) On differentiating w.r.t ,we get
` 2(x-1) +2 ( y - 2) (dy)/(dx) = 0 rArr (dy)/(dx) = (1-x)/(y-2)`
which is the required diffefrential equation ,