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

Options

A. ` xy' -y =0`
B. ` xy' +2y=0`
C. ` xy'-2y=0`
D. `xy' +y =0`

Answer

c

Explanation

The equation of the family of parabola having the vertex at origin and the axis along the positive Y - axis is
` x^(2) = 4ay ` …(i)
On differentiating Eq. (i) w.r.t x , we get
2x = 4ay'
On dividing Eq. (ii) by Eq. (i), we get
` (2x)/(x^(2)) = (4ay')/(4ay) rArr 2/x = (y')/y`
` rArr` xy' = 2y
` rArr xy' - 2y =0`
which it he required differentila equation .