From `x^2+y^2+2a x+2b y+c=0`, derive a differential equation not containing `a ,b ,a n d\ c`

Explanation

`x^{2}+y^{2}+2 a x+2 b y+c=0`


Differentiate equation (i) with respect to x,


`2 x+2 y y^{prime}+2 a+2 b y^{prime}=0`


Again differentiate equation with respect to x,


`2+2(y^{prime})^{2}+2 y y^{prime prime}+2 b y^{prime prime}=0 `


`1+(y^{prime})^{2}+y y^{prime prime}+b y^{prime prime}=0 `


`b=frac{-(1+(y^{prime})^{2}+y y^{prime prime})}{y^{prime prime}}`


`1+(y^{prime})^{2}+y y^{prime prime}+b y^{prime prime}=0`


...