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Mathematics-Online lexicon:

Parabola


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The points $ P=(x,y)$ of a parabola have the same distance from a given point $ F$ (focus) and a given line $ g$ (directrix).

\includegraphics[
width=12.4cm
]{a_parabel}

If $ F=(0,f)$ and $ g:\,y=-f$ , then we have for the coordinates

$\displaystyle 4f y = x^2
$

and

$\displaystyle r = \frac{4f\sin(\varphi)}{\cos^2(\varphi)}
$

for the polar coordinates of the points $ P$ .

Example:


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  automatically generated 3/28/2008