3x^2 +6y^2 = 18
Divide each term by 18 to make the right side equal 1:
3x^2/18 + 6y^2/18 = 1
Simplify each term:
x^2/6 + y^2/3 = 1
The form of an eclipse is written as (x-h)^2/a^2 + (y-k)^2/b^2 =1
Match the values in the ellipse to the standard form:
a = √6
b=√3
k = 0
h = 0
The center = (h,k) = (0,0)
Vertex is h +a, k = (√6,0) and (-√6,0)
Focus is h+c,k = (√3,0) and (-√3,0)
