Success message for typing in the correct equation for ellipse

Questions
1

I’m trying to display a “Success!” message when students enter an equation to match specific characteristics of an ellipse. Jay helped me with that message with parabolas that needed to go through 2 points. Now I want to match an equation to an equation or verify the latex entered matches f(x,y). What “angle” do I need to enter?

success issue

2

I figured out a way to make it work.
I verified the function went through the vertices.
success points

3

I was going to say f(x,y)=0 doesn’t evaluate anything.