Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

Explanation

As the centre of the circle lies on the y-axis. Let the center be (0, k). Hence, the equation of the circles with center (0, {k}) and radius 3 is,


`(x-0)^{2}+(y-k)^{2}=3^{2}`


`x^{2}+(y-k)^{2}=9` …...(i)


Differentiating equation with respect to x.


Hence,


`2 x+2(y-k) y^{prime}=0`


`y-k=-frac{x}{y^{prime}}`


Put the value of y-k in the equation (i).


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