Hyper-parabola

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A hyperbola is given with a parabola ax2  touching each branch of the hyperbola at single points. The task is to determine the value of a.

A formal proof of the general situation involves substituting the equation of the parabola into the equation of the hyperbola. The results in a quadratic in x2 which upon solving yields a very elegant result for the points of intersection.

The presentation and printed materials are supported by an interactive Geogebra file which has an option to show the equations of the curves.

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