Answer
If e=0, the conic section is a circle.
If e>0 and e<1, the conic section is an ellipse.
If e=1, the conic section is a parabola.
If e>1, the conic section is a hyperbola.
Work Step by Step
For a circle, $c=0$, so $e=0$.
For an ellipse, $cd$, so $e>1$.
