Form the differentials equation representing the family of ellipse having center at the origin and foci ion `x`-axis.

Explanation

Given,


`(x^2)/(a^2)+(y^2)/(b^2)=1`


Differentiating both sides w.r.t `x`


`(2x)/(a^2)+(2y)/(b^2)(dy)/(dx)=0`


Differentiating both sides w.r.t `x`


`(2)/(a^2)+(2)/(b^2)((dy)/(dx))^2+(2y)/(b^2)(dy^2)/(dx^2)=0`


By simplification in both equation


`(x)/(a^2)+(y)/(b^2)(dy)/(dx)=0`` \ \ \ ...(1)`


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