Solution

The given ellipse equation is:

\( 3x^{2} + 2y^{2} = 6 \)

Step 1: Write in standard form by dividing both sides by 6:

\(\frac{x^2}{2} + \frac{y^2}{3} = 1\)

Step 2: Identify \(a^2\) and \(b^2\):

• \(a^2 = \max(2, 3) = 3 \) → major axis along y-axis
• \(b^2 = \min(2, 3) = 2 \)

Step 3: Length of the major axis:

\( 2a = 2\sqrt{3} \)

Step 4: Coordinates of vertices along major axis (y-axis):

\( (0, \pm a) = (0, \pm \sqrt{3}) \)

Answer: Option B → \(2\sqrt{3}, (0, \pm \sqrt{3})\)