Q9 of 68 Page 910

Form the differential equation of the family of all circles touching the y-axis at the origin.

Equation of the family of all circles touching the y-axis at the origin can be represented by

(x-a)2+y2=a2, where a is an arbitrary constants.


(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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