Question

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

x² = 6y

Answer 1

The given equation is x² = 6y.

Here, the coefficient of y is positive. Hence, the parabola opens upwards.

On comparing this equation with x² = 4ay, we obtain

4a = 6 = a = `3/2`

∴ 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.e., y = `-3/2`

Length of latus rectum = 4a = 6