Find the equation in standard form of an ellipse with eccentricity 5/8, center at (0,0) and major axis on the x-axis and of length 16.

Use the standard equation for the ellipse, centered at (0,0):


(\frac x a)^2 + (\frac y b)^2 = 1.


You are told that the length of the major axis is 16, so this means the semi-major axis a is 8. Next, use the definition of eccentricity:


\epsilon = \sqrt {1 + (\frac b a )^2}


to determine the value for b.