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

Options

A. `(d^3x)/dy^3=0`
B. `(d^2x)/dy^2=c`
C. `(d^3x)/dy^3 + (d^2x)/dy^2=0`
D. `(d^2x)/dy^2 + 2(dy / dx)=c`

Answer

a

Explanation

The equation of the family of parabolas with axis parallel to axis of Y is
`(x-1)^(2) = A ( y -b)`
On differenting w.r.t x, we get
` 2(x-a) = Ay_(1)`
Again , on differenting w.r.t. x, we get
`2 = Ay_(2)` ltbRgt And again , on differentiating w.r.t x, we get
` y _(3) = 0`