Ellipse with Vertical Major Axis

Major axis along the y-axis, length 2a. Minor axis along the x-axis, length 2b. Vertices at (0, ±a) and (±b, 0). Foci at (0, ±c) where c² = a² − b².

Place the foci at $S(0, -c)$ and $S'(0, c)$ on the y-axis. The definition $PS + PS' = 2a$ with $a > c$ gives, by the same derivation as the horizontal case (with $x$ and $y$ interchanged):

$$\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1, \quad a > b > 0, \quad b^2 = a^2 - c^2$$

Elements:

Distinguishing the two standard forms: In $x^2/A^2 + y^2/B^2 = 1$, the larger denominator is $a^2$. If $A > B$, major axis is along x; if $B > A$, major axis is along y.