how to find the tangent line from a point to an ellipse Basically, I would like to calculate the purple line, (in the image).
The requirements are that it starts in the lower left point (25,820 )  or in the lower right point (symmetry). And it has to touch the ellipse (like in the image). (It is not allowed to cross|enter the ellipse). 
[ At the end, I've the know the point where the two purple line crosses each other, but that isn't a problem. But therefore I've to know both tangent points]

I think that this should be enough.
Thus can someone help me with calculating the tangent point? 

You can find tangency points with a simple geometric construction. Let $P$ be a point external to the ellipse, and $F$, $F'$ be its foci.


*

*Draw a circle centered at $F'$, with radius $2a$, equal to the major axis of the ellipse.

*Draw a circle centered at $P$, with radius $PF$; this circle will meet the other circle at two points $M$ ad $M'$.

*Join $F'M$ and $F'M'$: these segments cut the ellipse at the tangency points $Q$ and  $Q'$.
In other words: tangents $PQ$ and $PQ'$ are the perpendicular bisectors of segments $MF$ and $M'F$.

