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Mathematics-Online problems:

Interactive Problem 24: An Aerial Tramway Serving Several Mountain Stations

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
An aerial tramway is running from point $ A = (-6,0)$ up to two mountains that are given by the parabolas

$\displaystyle p_1: y = -x^2-3x+1, \hspace{5mm} p_2: y = -x^2+x+1 \ . $


\includegraphics{TdM_10_A1_bild1.eps}


Determine the position of the mountain stations $ B,\, C,$ and $ D$ such that the cables are tangent to these points.


Answer:

$ B \ = $ $ \Big($ $ ,$ $ \, \Big)$    
$ C \ = $ $ \Big($ $ ,$ $ \, \Big)$    
$ D \ = $ $ \Big($ $ ,$ $ \, \Big)$    
(The results should be correct to three decimal places.)


   

(From: Mathematics Contest 2010)
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  automatically generated: 8/11/2017