# Determine the equation for the ellipse with the points (2,0), (3,2sqrt2), (4,0), (3,-2sqrt(2) and the location for the foci.

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### 1 Answer

The points that lie on the ellipse are `(2,0)` , `(3, 2sqrt2)` , `(4,0)` and (3, -2*sqrt 2).

The minor axis of the ellipse is (4 - 2) = 2. The major axis of the ellipse is `(2*sqrt 2 + 2*sqrt 2) = 4*sqrt 2` .

The center of the ellipse is `(3, 0)`

The foci of the ellipse are at `(3, sqrt(32-4))` = `(3, 2*sqrt 7)` and at `(3, -2*sqrt 7)`

**The equation of the ellipse is **`(x - 3)^2/1 + y^2/8 = 1`