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 = – 16y

The given equation is x2 = -16y


Here, the coefficient of y is negative.


Hence, the parabola opens downwards.


On comparing this equation with x2 = -4ay, we get,


-4a = -16


⇒ a = 4


Thus,


Co-ordinates of the focus = (0,-a) = (0,-4)


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


Equation of directrix, x =a, then,


y = 4


Length of latus rectum = 4a = 16


4