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All ellipses have important key features.

- The
*vertices*of an ellipse are the intersection points between the ellipse and the line passing through the foci. - The
*major axis*of an ellipse is the segment connecting the vertices. - The
*center*of an ellipse is the midpoint of the major axis. - The
*co-vertices*of an ellipse are the intersection points between the ellipse and the line perpendicular to the major axis at the center of the ellipse. - The
*minor axis*of an ellipse is the segment connecting the co-vertices.

The above information can be illustrated in a diagram.

If the major axis of an ellipse is horizontal, the ellipse is called a *horizontal ellipse*. Conversely, if the major axis is vertical, the ellipse is called a *vertical ellipse*. Below are the general equations for these two types of ellipses.

$Horizontal Ellipsea_{2}(x−h)_{2} +b_{2}(y−k)_{2} =1Vertical Ellipseb_{2}(x−h)_{2} +a_{2}(y−k)_{2} =1 $

In these equations, $a$ and $b$ are half the lengths of the major and minor axes, respectively. Furthermore, in both cases, $(h,k)$ is the center of the ellipse.