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Mathematics-Online problems:

Interactive Problem 96: Intersecting Parabolas

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The parabolas in the figure below intersect at the points $ (0,2)$ and $ (\pm 1,0)$ perpendicularly.
\includegraphics[width=0.8\linewidth]{parabel.eps}

For the parabolas of the form

$\displaystyle y = ax^2 + bx + c $

find their coefficients, the coordinates of the intersection points $ (\pm u,v)$ where $ v>0$, and determine the area of the shaded region.


Answer:

Coefficients of the parabolas:

Coordinates of the intersection points: $ u = $ , $ v =$

Area: $ A = $

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

   

(From: Day of Mathematics 1999)
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  automatically generated: 8/11/2017