Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.

To solve this problem you must apply the proccedure showb below:

1. You have the following equation:

2x^2+9y^2=18

2. Dividing the equation by 18, you have:

(x^2/9) + (y^2/2) = 1

3. The center is:

[ (x-0) ^2/9]3^2[ (y-0) ^2/√2]=1

(h, k) = (0,0)

The center is (0,0)

4. The vertices are:

a^2=9

a=3

Vertices: (-3,0) and (3,0)

5. The foci is:

c^2=a^2-b^2

c = √7

The foci is: ( - √7,0) and (√7,0)