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Form the differential equation of all th...

Form the differential equation of all the circles whose centre is at origin.

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Let the radius of the circle is `x^(2) - y^(2) = r^(2)` differentiating `2x + 2y y' = 0`
`rArr x + y y' = 0`
This equation is free arbitrary constant
`:.` It is the required differential equation.
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