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I have two sets of points and i want draw an parabolic arc between two points and also to find the intermediate points which the parabolic path is drawn....

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In the above image you can see the curve path on two sides....since it is an image,i can't trace out the exact curve..i can get the starting,middle and end point of the one side of the curve.Is it possible to draw the curve and also get the each points of the curve...

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    Perhaps you could be more specific and/or give an example? In the real plane, a parabola is uniquely determined by **three** points (non-collinear if you want to avoid degenerate parabolas) and you can find this parabola via interpolation. If you have "two sets of points" I would imagine you might have more than three total in which case there may not be a parabola that traverses all of them.2011-09-09
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    I don't think I understand. There are an infinite family of parabolas between two given points and they can be solved for easily, but what else is being asked here?2011-09-09
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    i have updated my qn.....2011-09-09
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    In general a parabola has the equation $a x^2 + 2 b x y + c y^2 + d x + e y + f = 0$ where $ac = b^2$, $a^2 + c^2 > 0$ and $d^2 + e^2 > 0$. There are 5 degrees of freedom here, but since we can multiply the equation by a nonzero constant the curve has 4 degrees of freedom. Specifying any two distinct points in the plane for the parabola to pass through still leaves 2 degrees of freedom, i.e. a 2-parameter family of parabolas through the two points. So which of these infinitely many parabolas do you want?2011-09-09
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    If i know the 3 points(starting,middle and ending point).is it possible to trace the curve...2011-09-09
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    Maybe you should have just updated your [previous question](http://math.stackexchange.com/questions/62870) instead.2011-09-09

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