I have a parabola centered at x=0, equation: y = a*x^2 + c, where a is always negative and c always positive.(adsbygoogle = window.adsbygoogle || []).push({});

I need to find a way to calculate a and c, if i know: the arc length above the x axis, and the base width, knowing the base width i also know the x axis intersections x1,2 = -+base_width/2;

The problem is the formulas for the arc length are too complicated for me to 'play around' with..

For example the base_width/height formula from http://www.had2know.com/academics/parabola-segment-arc-length-area.html:

arc_len = 0.5√16h²+w² + [w²/(8h)][Ln(4h + √16h²+w²) - Ln(w)]

I tried to solve for h with wolfram alfa, and mathematica, neither helped..

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# How to calculate the height of a parabola, given base width and arc length?

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