i have arc of ellipse with start and end point of ellipse. And also i have radius's of ellipse. using this data how can i find center of ellipse? EX:: arc with (140,50) as start point and (240,100) as end points, (200,50) as radius's of ellipse. from this given data how could i find center of ellipse?
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I don't think this is possible. Let $P$ and $Q$ be the given two points. Take an ellipse with given semi-axes $a$ and $b$ that passes through $P$ and $Q$. Imagine $P$ and $Q$ as pins sticking in the floor, and the ellipse is a piece of cardboard that's touching both of them. Clearly you can "slide" the ellipse around, keeping it in contact with the two pins. The sliding motion will change the center.
I'm sure that an argument could be constructed that is more mathematically rigorous. But the physical argument works OK for me.
Here's a picture of two ellipses, both with semi-axes (200,50) that both pass through your two given points. Obviously they have different centers.
Using the "sliding" process I described, you can produce an infinite number of ellipses with this same size through these same two points. So, your problem is unsolvable.
The original question (which I answered above) was about the case where the orientation of the ellipse is not known. If the orientation is known/fixed, then the question has been answered already here.