MathematicsMedium38×since 2002Q3504The differential equation of the family of circles passing through the origin and having centre at the line y=xy=xy=x is :A(x2−y2+2xy)dx=(x2−y2+2xy)dy\left(x^2-y^2+2 x y\right) \mathrm{d} x=\left(x^2-y^2+2 x y\right) \mathrm{d} y(x2−y2+2xy)dx=(x2−y2+2xy)dyB(x2+y2−2xy)dx=(x2+y2+2xy)dy\left(x^2+y^2-2 x y\right) \mathrm{d} x=\left(x^2+y^2+2 x y\right) \mathrm{d} y(x2+y2−2xy)dx=(x2+y2+2xy)dyC(x2+y2+2xy)dx=(x2+y2−2xy)dy\left(x^2+y^2+2 x y\right) \mathrm{d} x=\left(x^2+y^2-2 x y\right) \mathrm{d} y(x2+y2+2xy)dx=(x2+y2−2xy)dyD(x2−y2+2xy)dx=(x2−y2−2xy)dy\left(x^2-y^2+2 x y\right) \mathrm{d} x=\left(x^2-y^2-2 x y\right) \mathrm{d} y(x2−y2+2xy)dx=(x2−y2−2xy)dyCheck answerSkip