The equation of our ellipse is:
[tex]100 x^2 + 64 y^2 = 6400[/tex] (1)
First, let's reduce the equation of the ellipse to the standard form:
[tex] \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 [/tex]
To do that, we should divide both terms of equation (1) by 6400, and we get:
[tex] \frac{x^2}{64}+ \frac{y^2}{100}=1 [/tex]
This is a vertical ellipse (because [tex]b^2 \ \textgreater \ a^2[/tex]) centered in the origin, and so the distance of its foci from the origin (on the y axis) is given by
[tex]c= \sqrt{b^2-a^2}= \sqrt{(100)-(64)}=6[/tex]
Therefore, the position of the two foci is (0,6) and (0,-6)
