In each of the following, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

x² = 6y

The given equation is y² = 6y

Here, the coefficient of y is positive.

Hence, the parabola opens upwards.

On comparing this equation with y² = 4ay, we get,

4a = 6

⇒ a =

Thus,

Co-ordinates of the focus = (0,a) =

Since, the given equation involves x², the axis of the parabola is the y-axis.

Equation of directrix, y =-a, then,

y =

Length of latus rectum = 4a = 6