GeoGebra has a built-in tool to draw an ellipse, and compute the equation of the ellipse. 
     GeoGebra Instruction 1
Algebra     View     and         Graphics     View     under         View     in         Menu.         Ellipse Graphics     View.         These         will         be         the         focal         points.         Midpoint     or     Center The ellipse will now appear in Graphics View. The equation of the ellipse will appear in a row in Algebra View as well.