What are the foci of the ellipse given by the equation 100x^2 + 64y^2 = 6 400?

The equation of our ellipse is:

(1)

First, let's reduce the equation of the ellipse to the standard form:

To do that, we should divide both terms of equation (1) by 6400, and we get:

This is a vertical ellipse (because ) centered in the origin, and so the distance of its foci from the origin (on the y axis) is given by

Therefore, the position of the two foci is (0,6) and (0,-6)