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# Parabolas

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## katie oliver

on 6 May 2010

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#### Transcript of Parabolas

Parabola History
Menaecnmus, a pupil of Plato & Eudoxus, attempted to duplicate the cube to find a side of a cube that has a volume double the size of a given cube. He solved it by finding the intersection of the two parabolas x²=y and y²=2x.Later, Apollonius gave the parabola its name after reading Euclid's writings on the conic section. The focus and directrix of the parabola were suggested by Pappus.
Standard Equation Formulas
-horizontal:
Ay²+Dx+Ey+F=O
-vertical:
Ax²+Dx+Ey+F=O

Famous astronomer Galileo found that any object thrown flys in a parabolic path. Real world examples:
mirrors in reflecting telescopes
human eye Horizontal Graphing Formula:
-centered at origin
(y-O)²=4p(x-O)
-centered at (h,k)
(y-k)²=4p(x-h)

Vertical Graphing Formula:
-centered at origin
(x-O)²=4p(y-O)
-centered at (h,k)
(x-h)²=4p(y-k) A parabola is a set of points (x,y) that are the same distance from a fixed line (directrix) and a fixed point (focus). The vertex is the midpoint of the segment connection focus and directrix. The axis of symetry is the line passing through the focus and vertex.
-vertical parabolas have a vertical aos
-horizontal parabolas have a horizontal aos

The directrix is always parallel to the aos Type:
The type of parabola is determined by the letter that is NOT squared.
-horizontal if (x-h) is not squared
-vertical if (y-k) is not squared |p| in the graphing formula represents the distance from vertex to focus and distance from vertex to directrix.
2|p| is the distance from focus to LRE
4|p| is the length of the LRE segment
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