Question

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 6y

Answer 1

Here, the coefficient of y is positive. Hence, the parabola opens upwards.
On comparing this equation with x² = 4ay, we obtain

∴Coordinates of the focus = (0, a) =(0,3/2)

Since the given equation involves x2, the axis of the parabola is the y-axis.
Equation of directrix, y = a i c., y = -3/2
Length of latus rectum = 4a = 6