Find the center, vertices, and foci of the ellipse with equation 2x2 + 6y2 = 12.
Center: (0, 0); Vertices: (-V6,0),(V6,0); Foci: (-2, 0), (2,0)
Center: (0, 0); Vertices: (0, -6), (0, 6);
Center: (0, 0); Vertices: (0, -16),(0,16); Foci: (0, -2), (0, 2)
Center: (0, 0); Vertices: (-6, 0), (6, 0);

Centre: (0,0); vertices: (-√6,0),(√6,0); foci: (-2,0), (2,0)  

Step-by-step explanation:

2x² + 6y² = 12

We must convert this to the standard form of an ellipse

h = 0; k = 0; a = √6; b = √2

The centre is at (h,k) = (0,0)

a > b, so the major axis along the x-axis

The vertices are at (±a,0), that is, they are at (-√6,0) and (√6,0).

c² = a² - b² = 6 - 2 = 4

c = 2

The foci are at (-2,0) and (2,0).

The graph of your ellipse shows the centre at (0,0), the vertices at (-√6,0) and (√6,0), and the foci at (-2,0) and (2,0).

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step-by-step explanation: