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)