Asked by Haymanot
Determine equation of the ellipse if the distance between its foci is 2sqrt5 and the end points of its minor axis are (-1,-2) and (3,-2).
Answers
Answered by
oobleck
the minor has has length 2b, so
b = 4/2 = 2
c = √5
so a^2 = b^2 + c^2 = 9
The center is midway between the foci, at (1,-2)
The minor axis is horizontal, so the major axis is vertical, making the equation
(x-1)^2/4 + (y+2)^2/9 = 1
Confirm at
https://www.wolframalpha.com/input/?i=%28x-1%29%5E2%2F4+%2B+%28y%2B2%29%5E2%2F9+%3D+1
and click on Properties
b = 4/2 = 2
c = √5
so a^2 = b^2 + c^2 = 9
The center is midway between the foci, at (1,-2)
The minor axis is horizontal, so the major axis is vertical, making the equation
(x-1)^2/4 + (y+2)^2/9 = 1
Confirm at
https://www.wolframalpha.com/input/?i=%28x-1%29%5E2%2F4+%2B+%28y%2B2%29%5E2%2F9+%3D+1
and click on Properties
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