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?
The equation of an ellipse with axes parallel to the axes of coordinates, center at (alpha, beta) and semi-axes a and b is
If a < b, the ellipse is vertical, with major axis parallel to the y-axis.
In this case,
Here, a = 2 < b = 5. So, the e is given by