How do I graph the ellipse with the equation #−x+2y+x^2+xy+y^2=0#?
Remove the cross-product term, then graph on the new coordinate axes.
There are various forms and formulas used for conic sections. I use
So we re-write:
Our new coordinate system will be denoted
Replace and simplify.
Now treat it like a non-rotated ellipse. Find center and vertices and graph on the new axes.