The differential equation of all parabolas whose axis are parallel to the y-axis is

Options

A. `y_(2)=2y_(1)+x`
B. `y_(3)=2y_(1)`
C. `y_(2)^(3)=y_(1)`
D. None of these

Answer

B

Explanation

The equation of the familiy of parabola with axis parallel to axis of y is `(x-a)^(2)=A(y-b)`
On differentiable w.r.t.x. we get
2(x-a)=`Ay_(1)`
Again differentiating w.r.t.x, we get
`2=Ay_(2)`
On again differentiating w.r.t.x. we get
`y_(3)=0`