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Question -

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.



Answer -

The equation of the family of ellipses having foci on the y-axis and the centre at origin is as follows:

Differentiating equation (1) with respect to x, we get:
 
Again, differentiating with respect to x, we get:
 
Substituting this value in equation (2), we get:
 
This is the required differential equation.

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