Question

How would I solve for the vertex, directrix and focus coordinates of this parabola `x^2 − 32y = 0`?

Answer 1

`x^2 -32y=0` is `(x-0)^2=32(y-0)`= 4(8)(y-0)

This vertical parabola has vertex at (0,0). Axis of symmetry is the line x=0, that is the y axis. The distance of the focus from the vertex is 8 units and it lies on axis of symmetry. Its coordinates would therefore be (0,8). The directrix would then be the line y= -8