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Mathematics-Online course: Vector Calculus - Quadratic Curves

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$ .

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  automatically generated 10/30/2007