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Mathematics-Online course: Prepcourse Mathematics - Linear Algebra and Geometry - Quadratic Curves

Satellite TV

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Parallel rays perpendicular to the directrix are bundled in the focus. This property is used to amplify incoming signals in parabol aerials ('satellite dishes').
\includegraphics[ width=12.4cm ]{b_satellitentv}

To prove this property, first of all, we see that

$\displaystyle \overrightarrow{FP} + \overrightarrow{QP} = \left(\left(\begin{a... ... -f\end{array}\right)\right)= \left(\begin{array}{c}x\\ 2y\end{array}\right) $

is parallel to the direction of the tangent in point $ P$ ,

$\displaystyle \left(\begin{array}{c}1\\ x/(2f)\end{array}\right)\, . $

Since

$\displaystyle \vert\overrightarrow{FP}\vert = \vert\overrightarrow{FQ}\vert\, , $

it follows equality of the angles $ \sphericalangle(F,P,R)$ and $ \sphericalangle(R,P,Q)$ , where $ R$ is the intersection point of the tangent and $ g$ .
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  automatically generated 10/23/2009