Q10 of 68 Page 910

From the differential equation of the family of circles having centers on y-axis and radius 2 units.

Equation of the family of circles having centers on y-axis and radius 2 units can be represented by

(x)2+(y – a)2= 4, where a is an arbitrary constant.


(1)


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





Substituting the value of a in equation (1)





Rearranging the above equation



This is the required differential equation.


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