Algebra

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

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  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.

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