standard form of the equation of an ellipse:

where b²= a² - c²

center (0,0) (0,0)major axis on x-axis, length 2a on y-axis, length 2aminor axis on y-axis, length 2b on x-axis, length 2bfoci (±c,0) (0,±c)vertices (±a,0) (0,±a)covertices (0,±b) (±b,0)</span>

a is always larger than b; and a,b, and c are related by c²= a² - b²

ex.
Graph 9x²+ 4y²= 36

which is an ellipse.
a² = 9 ; b² = 4
center (0,0)
major axis: y-axis
vertices: (0, ± 3)
covertices: (± 2,0)

Graph 9x² + 25y² = 225

a²= 25 ; b²= 9
center (0,0)
major axis: x-axis
vertices: (± 5,0)
covertices (0,± 3)

c²= a² - b²
c²= 25 - 9
c² = 16

foci: (± 4,0)