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?

1 Answer
A. S. Adikesavan
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#.

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#.. .

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