The differential equation of all ellipse centered at the origin axis being coordinate axes is:

$xyy_2-xy_1^2+yy_1=0$ $xyy_2+xy_1^2+yy_1=0$ $xyy_2+xy_1^2+yy_1=0$ None of these

$xyy_2+xy_1^2+yy_1=0$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1⇒\frac{x}{a^2}+\frac{y}{b^2}\frac{dy}{dx}=0$ … (i) $\frac{1}{a^2}+\frac{1}{b^2}(y_1^2+yy_1)=0$ … (ii) From (i) and (ii); $\frac{1}{2}(yy_1-xy_1^2-xyy_2)=0⇒xyy_2+xy_1^2+yy_1=0$