Most recent change of Parabola
Edit made on February 13, 2009 by derekcouzens at 20:40:30
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HEADERS_END
[[[> IMG:parabola5.png ]]]
The Parabola is a plane curve. The Parabola is a conic section.
The parabola is defined as the path of a point (locus) which moves such that its distance from a fixed point (called the focus) is equal to its distance from a fixed line (called the directrix).
When the directrix is x = -a and the focus is ( a, 0) the parabola will have the equation in Cartesian Coordinates EQN:y^2=4ax
Rays parallel to the axis of symmetry of a parabolic mirror are reflected through the focus which makes these devices very useful in optical instruments.
Similarly, rays that originate at the focus will produce a parallel beam thereby making parabolic mirrors useful in torches and searchlights.
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Exercise
Enrichment task
Show that when the directrix is x = -a and the focus is ( a, 0) then the equation of the curve is EQN:y^2=4ax
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One of the Named Curves on this site.
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One of the Enrichment tasks on this site