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 a circle is
`x^(2)+(y-a)^(2)=a^(2)" "...(i)`
`2x+2y(dy)/(dx)-2a(dy)/(dx)=0" "...(ii)`
From Eqs. (i) and (ii)
`(dy)/(dx)=(2xy)/(x^(2)-y^(2))`
`implies(x^(2)-y^(2))(dy)/(dx)-2xy=0`