The general equation of a conic section is:



The discriminant  is used to determine which 
conic section will result. 

1. If the discriminant is less than zero we have 
   (a). a circle if B = 0 and A = C, or 
   (b). an ellipse otherwise.
2. If the discriminant is equal to zero we have a parabola.
3. If the discriminant is greater than zero we have a hyperbola.


Your equation is:



We put the term in  in between the terms in , and get 0 on the right, so it will be in 
the same form as above:



we have  

,





,  ,  

So the discriminant = 

  

Since the discriminant is negative, by the rules at the
top we can conclude the equation represents an ellipse.

Edwin