Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
36x² + 4y² = 144.

= 1 or = 1

since the denominator of x² < denominator of y², the major axis is along the y-axis. Comparing the given equation with the standard equation

= 1

we have b = 2 and a = 6

Also, c = = = = 4

and e = = = =

Hence the foci, (0, c) and (0, c) are (0, 4) and (0, -4). Vertices, (0, a) and (0, a) are (0,6) and (0,-6); the length of the major axis, 2a is 12 units; the length of the minor axis, 2b is 4 units and the eccentricity of the ellipse, e is .

The length of latus rectum, is = units.