A Parabola is the set of all points (locus) equal distance from a fixed line (Directrix) and a fixed point (Focus). The Vertex is equal distance from the directrix and the focus. The equation of a parabola is derived from the distance formula. The standard equation of a parabola with vertex at the origin and directrix horizontal is

solving for Y

the curve opens up

the curve opens down

A parabola has the useful feature that a line parallel to the symmetry axis striking the parabola at any point is reflected onto the focus.

recasting our most common parabola

becomes

the focus is at (0, 0.25)

the directrix is at Y=-0.25

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