(h,k) is the center of the ellipse,
a is the distance between the vertex and the center, and
b is the distance between the endpoint of minor axis and the center.
Look at the graph below, point A is the center.
When a > b, points B1 and B2 are the vertices, points C1 and C2 are the endpoints of minor axis, and F1 and F2 are the foci.
When a < b, points C1 and C2 are the vertices, points B1 and B2 are the endpoints of minor axis, and F3 and F4 are the foci.
The line segment which connects the vertices is called as major axis. The line segment which is shorter, perpendicular to the major axis and passes through the center is called the minor axis.
You may slide the values of a, b, h or k to observe the changing of the graph.
Betty, Created with GeoGebra