If the conic is non-degenerate, then: if , the equation represents an ellipse; if and , the equation represents a circle, which is a special case of an ellipse; if , the equation represents a parabola; if , the equation represents a hyperbola; if we also have , the equation represents a rectangular hyperbola.
If the conic is non-degenerate then if  the equation represents an ellipse; if and  the equation represents a circle which is a special case of an ellipse; if  the equation represents a parabola; if  the equation represents a hyperbola; if we also have  the equation represents a rectangular hyperbola