Question

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?

Answer 1

`(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`.

If a < b, the ellipse is vertical, with major axis parallel to the y-axis.

In this case, `a^2=b^2(1-e^2` gives the eccentricity e of the ellipse.

Here, a = 2 < b = 5. So, the e is given by

`4 = 25(1 - e^2). e=sqrt 21/5`.. .