The differential equation of the family of circles passing through the origin and having centres on the x-axis is

Options

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

Answer

a

Explanation

The equation of a circle passing through the origin and having their centres on the X - axis is
` x^(2) +y^(2) + 2 gx = 0" "` … (i)
where g is an arbitrary constant .
On differenting w.r.t . X, we get
` x + y (dy)/(dx) + g = 0 `
` rArr y^(2) = x^(2) + 2xy (dy)/(dx)`