# How do I graph the ellipse with the equation #−x+2y+x^2+xy+y^2=0#?

##### 1 Answer

Remove the cross-product term, then graph on the new coordinate axes.

#### Explanation:

There are various forms and formulas used for conic sections. I use

And

So we re-write:

We get:

so

and

Our new coordinate system will be denoted

Using

Replace and simplify.

I get

Now treat it like a non-rotated ellipse. Find center and vertices and graph on the new axes.