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An attempt to find the equation of an ellipse inscribed in a given triangle. 
The program works on the basis of the ELS procedure.  After the procedure works, the  solutions are filtered.
ELS procedure solves the system of equations f1, f2, f3, f4, f5 for the coefficients of the second-order curve.
The equation f1 corresponds to the condition that the side of the triangle intersects t a curve of the second order at one point.
The equation f2 corresponds to the condition that the point x1,x2  belongs to a curve of the second order.
Equation f3 corresponds to the condition that the side of the triangle is tangent to the second order curve at the point x1,x2.
The equation f4 is similar to the equation f2, and the equation f5 is similar to the equation f3.
FOR_ELL_ТR_PROCE.mw
For example
animation triangle ellipse inscribed

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