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

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Solution

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

∴Coordinates of the focus = (0, a) =

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

Equation of directrix,

Length of latus rectum = 4a = 6

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