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Mathematics-Online problems:

Interactive Problem 201: Hyperbola Tangent to a Parabola

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The figure shows the parabola $ P: y = 4 - \dfrac{x^2}{3}$, that is tangent to the hyperbola $ H: y = \dfrac{a}{x}$ at $ B$ and intersects it at $ S$.


\includegraphics[width=.6\linewidth]{TdM_12_A1_bild}


Find the parameter $ a>0$ as well as the point of tangency $ B$ and the point of intersection $ S$ .


Answer:

$ a = $       
$ B = $ $ \big($ , $ \big)$  
$ S = $ $ \big($ , $ \big)$  

(The results should be correct to four decimal places.)


   

(From: Mathematics Contest 2012)
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  automatically generated: 3/12/2018