SOLUTION: The foci are at (3, 5) and (1, 5), and the ellipse has eccentricity 0.25.

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Question 1192548: The foci are at (3, 5) and (1, 5), and the ellipse has eccentricity 0.25.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The foci are (1,5) and (3,5); so the center is (2,5), and the distance from the center to each focus, c, is 1.

The eccentricity 0.25=1/4 is c/a, where a is the semi-major axis; so a=4.

c^2=a^2-b^2 where b is the semi-minor axis, so b is sqrt(15).

The major axis is horizontal, so the equation is

%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1

%28x-2%29%5E2%2F16%2B%28y-5%29%5E2%2F15=1