What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?

The ordinary equation of a ellipse is given as follows:

[tex]\frac{ x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

Being:

a: Semi-major axis 
b: Semi-minor axis

Our equation is:

[tex]100 x^{2} + 64y^{2} = 6400[/tex]

Multiplying this equation by: 

[tex] \frac{1}{(100)(64)} [/tex]

Then:

[tex]\frac{ x^{2}}{64} + \frac{y^{2}}{100} = 1[/tex]

We can see that:

[tex]a = \sqrt{100} = 10[/tex]
[tex]b = \sqrt{64} = 8[/tex]

Then the semi-major axis is on the y-axis, and the focus are located there, so:

[tex]F_{1} = (0,c)[/tex]
[tex]F_{2} = (0,-c)[/tex]

We also know that the relation between a, b and c is:

[tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]c^{2} = 100 - 64 = 36[/tex]
[tex]c = \sqrt{36} = 6[/tex]

Then, the focus are:

[tex]F_{1}(0,6)[/tex]
[tex]F_{1}(0,-6)[/tex]