How can I find the center of ellipse given an Arc and ellipse radii? [duplicate]

I have an arc with start and end points and also I have width and height of the ellipse. Using these can I find center of the ellipse?

hi Stefan,

how can i calculate $(x,y)$ center , can u give idea?

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migrated from mathematica.stackexchange.comAug 7 '13 at 10:46

This question came from our site for users of Mathematica.

marked as duplicate by Adriano, Dan Rust, azimut, Start wearing purple, Nick PetersonAug 7 '13 at 11:38

This question was marked as an exact duplicate of an existing question.

Is this about implementation in Mathematica? What do you mean by "I have arc"? – Kuba Aug 7 '13 at 10:37

If you only have the start and end point, you can only solve for two parameters ($x$ and $y$ of your center). If you know the alignment of your ellipse, this is enough and can be calculated by solving the equation system given from the equation of the ellipse and your points.
If the ellipse is rotated, you also need the rotation angle $\alpha$ and thus a third point from your arc.
@SushmithaSush You should look at the link shown in the "duplicate question"-part of your question. The main idea is to take the ellipse equation ($(x-x_0)^2/a^2+(y-y0)^2/b^2=r^2$) and put your known points and lengths in. This should give you the center $(x_0,y_0)$. – Stefan Aug 7 '13 at 13:19