Find the center, vertices, and foci of the ellipse with equation 3x2 + 6y2 = 18.

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)

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

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