Q. 74.0( 36 Votes )

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Answer :

We know that the equation of the parabola having the vertex at origin and the axis along the positive y- axis is

x2 = 4ay ------(1)



Now, differentiating equation (1) w.r.t. x, we get,


2x = 4ay’ -----(2)


On dividing equation (2) by equation (1), we get,




xy’ = 2y


xy’ – 2y = 0


Therefore, the required differential equation is xy’ – 2y = 0.


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