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find standard form given eccentricity and center of ellipse

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):

$<br /> (\frac x a)^2 + (\frac y b)^2 = 1.<br />$

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:

$<br /> \epsilon = \sqrt {1 + (\frac b a )^2}<br />$

to determine the value for b.

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