Form the differential equation of the family of circles touching the y-axis at origin.

Explanation

If the circles touches `Y`-axis at origin then its centre will lie on `X`-axis.
`:.` equation of circle
`(x-h)^(2)+(y-0)^(2)=h^(2)`
`implies x^(2)+y^(2)-2hx=0`……..`(1)`
differentiate w.r.t.x,
`2x+2y(dy)/(dx)-2h=0`
`implies 2h=2x+2y(dy)/(dx)`
Put this value in equation `(1)`,
`x^(2)+y^(2)-x(2x+2y(dy)/(dx))=0`
`implies y^(2)-x^(2)-2xy(dy)/(dx)=0`