Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.

Options

A. ` (x^(2)-y^(2))(dy)/(dx) - 2xy=0`
B. `(x^(2)-y^(2))(dy)/(dx)+2xy=0`
C. ` (x^(2)-y^(2))(dy)/(dx)-xy = 0`
D. ` (x^(2) -y^(2)) (dy)/(Dx) + xy = 0`

Answer

a

Explanation

Equation of the circles that through the origin and whose centre lie on X -a xis is
`x^(2)+(y-a)^(2)=a^(2)" " `(i)
` rArr x^(2) +y^(2) = 2ay +a^(2) = a^(2)`
` rArr 2x + 2y (dy)/(dx) - 2a (dy)/(dx)=0" "` ...(ii)
From Eqs. (i) and (ii)
` (dy)/(dx) = (2xy)/(x^(2)-y^(2))rArr (x^(2)- y^(2)) (dy)/(dx) - 2xy =0`