Question

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

Answer 1

The given equation is 36x² + 4y² = 144.

It can be written as

Here, the denominator of is greater than the denominator of.

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing equation (1) with, we obtain b = 2 and a = 6.

Therefore,

The coordinates of the foci are.

The coordinates of the vertices are (0, ±6).

Length of major axis = 2a = 12

Length of minor axis = 2b = 4

Length of latus rectum