# How can a general equation tell me whether a conic section is a circle or an ellipse?

${\left(x - h\right)}^{2} / {a}^{2} + {\left(y - k\right)}^{2} / {b}^{2} = 1$
If $a = b$ then you have a circle.
If $a > b$ then you have an ellipse where the $x$ axis is the major axis.
If $b > a$ then you have an ellipse where the $y$ axis is the major axis.