Obtain the differential equation of the family of circles passing through the point (a,0) and (-a,0).

Explanation

`x^2+(y-h)^2=h^2+a^2`

differentiate with respect to x

`2x+2(y-h)y'=0`

`x=(y-h)y'`

`y-h=x/y`

`h=y-x/y`

`x^2+(y-y+x/y')^2=y^2-(2xy)/y'+x^2/y'+a^2`

`x^2+x^2/y'^2=y^2-(2xy)/y'+x^2/y'^2+a^2`

...