In Example 2, interchange the 4 and 9; find the vertices, ends of the minor axis, and foci; and sketch the ellipse.

Data from Example 2

The equation of the ellipse

has the larger denominator, 9, under the y². Therefore, it fits the form of Eq. (21.19) with a² = 9 and b² = 4. This means that the vertices are (0, 3) and (0,−3), and the minor axis extends from (−2, 0) to (2, 0). In turn, we know that c² = a² − b² = 9 − 4 = 5 and that the foci are (0, 5) and (0,− 5). This ellipse is shown in Fig. 21.61.

b +3 y2 4 9 + = 1 || a 2