Parabola/Proofs

Parabola/Proofs

:"This mathematics article is devoted entirely to providing mathematical proofs and support for claims and statements made in the article parabola. This article is currently an experimental vehicle to see how well we can provide proofs and details for a math article without cluttering up the main article itself. See for some current discussion. This article is "experimental" in the sense that it is a test of one way may be able to incorporate more detailed proofs in Wikipedia."

"Note": Proof is given in a two-column format.

Definitions

*Directrix: line "l"
*Focus: point "f" which is not contained by line "l"
*Parabola: the locus of points in a plane which are equidistant from line "l" and a point "f"
*Axis of symmetry: the line which is both perpendicular to the directrix and contains point "f"
*Vertex: the locus of points which lie on a the parabola and are points on the axis of symmetry

Proof

Prove for point ("x","y") on a parabola with focus ("h","k"+"p") and directrix "y"="k"-"p", that:
(x - h)^2 = 4p(y - k)
and that the vertex of this parabola is ("h","k")


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