# What is the equation, in standard form, of a vertical ellipse centered at (–8, 12) with a major axis of length 10 and a minor axis of length 4?

Apr 28, 2016

(x+8)^2/2^2+(y-12)^2/5^2=$1. #### Explanation: The equation of an ellipse with axes parallel to the axes of coordinates, center at (alpha, beta) and semi-axes a and b is (x-alpha)^2/a^2+(y-beta)^2/b^2=$1.
In this case, a^2=b^2(1-e^2 gives the eccentricity e of the ellipse.
$4 = 25 \left(1 - {e}^{2}\right) . e = \frac{\sqrt{21}}{5}$.. .