Focus Of A Parabola - Mathwords

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Focus of a Parabola

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

Note: For a parabolic mirror, all rays of light emitting from the focus reflect off the parabola and travel parallel to each other (parallel to the axis of symmetry as well).

Upward-opening parabola with vertex (h,k) and focus point p above vertex. Formulas: vertical 4p(y-k)=(x-h)²; horizontal... Parabola with point P, focus inside curve, directrix below. L1 (P to focus) = L2 (P to directrix), shown with arrows.