Q. 104.2( 65 Votes )

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

Answer :


Let the centre of the circle on y – axis be (0,b).


We know that the differential equation of the family of circles with centre at (0, b) and radius 3 is: x2 + (y- b)2 = 32


x2 + (y- b)2 = 9 ----(1)


Now, differentiating both sides w.r.t. x, we get,


2x + 2(y – b).y’ = 0


(y – b). y’ = x


y – b =


Thus, substituting the value of ( y – b) in equation (1), we get,




x2((y’)2 + 1) = 9(y’)2


(x2 – 9)(y’)2 + x2 = 0


Therefore, the required differential equation is (x2 – 9)(y’)2 + x2 = 0


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