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Question -

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



Answer -

The equation of the family of hyperbolas with the centre at origin and foci along the x-axis is:

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

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