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

\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} + {{\rm{y}}^2}\)

\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} - {{\rm{y}}^2}\)

\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{y}}^2} - {{\rm{x}}^2}\)

\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} + {{\rm{x}}^2} + {{\rm{y}}^2} = 0\)

The differential equation of the family of circles passing through the

1.	The differential equation of the family of circles passing through the origin and having centres on the x-axis is
A.	\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} - {{\rm{y}}^2}\)
B.	\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{y}}^2} - {{\rm{x}}^2}\)
C.	\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} + {{\rm{y}}^2}\)
D.	\(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} + {{\rm{x}}^2} + {{\rm{y}}^2} = 0\)
Answer» C. \(2{\rm{xy}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {{\rm{x}}^2} + {{\rm{y}}^2}\)