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

Options

A. `2y_(1)-y=0`
B. `2y_(1)+xy=0`
C. `xy_(1)-2y=0`
D. `yy_(1)-2x=0`

Answer

C

Explanation

The equation of the family of parabolas having vertex at the origin and y-axis as the axis of symmetry is
`y=ax^(2)`
`rArr" "(dy)/(dx)=2ax`
`rArr" "(dy)/(dx)=(2y)/(x)" "[because y=ax^(2)rArr a=y//x^(2)]`
`rArr" "xy_(1)-2y=0`
This is the requried differential equation.