What is the focus of a parabola? And can the directrix be anywhere not on the focus? I'm confused!

Answer 1

The focus of a parabola of the form
y = a x^2 is at x = 0 and y = 1/(4a)

The directrix is always a straight line outside the parabola and perpendicular to its axis. For the case of a y= a x^2 parabola, the directrix is at
y = -1/(4a)

All points on a parabola are equidistant from the focus and the directrix.