Q. 154.5( 2 Votes )

Form the differential equation of the family of an ellipse having foci on the y-axis and centers at the origin.

Answer :

Equation of the family of an ellipse having foci on the y-axis and centers at the origin can be represented by

(1)


Differentiating the above equation with respect to x on both sides, we have,






Again differentiating the above equation with respect to x on both sides, we have,




Rearranging the above equation



This is the required differential equation.


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