Question

The length of major axis and coordinate of vertices for the ellipse \( 3x^2 + 2y^2 = 6 \) respectively are:

• A. \( 2\sqrt{2}, (0, \pm\sqrt{3}) \)
• B. \( 2\sqrt{3}, (0, \pm\sqrt{3}) \)
• C. \( 2\sqrt{2}, (\pm\sqrt{3}, 0) \)
• D. \( 2\sqrt{3}, (\pm\sqrt{3}, 0) \)

Hint:

For ellipses, identify the values of \( a \) and \( b \) to determine the length of the axes and the location of the vertices.

Answer 1

The Correct Option is A

Step 1: Rewrite the ellipse equation in standard form.
The given equation is \( 3x^2 + 2y^2 = 6 \), which we can divide by 6 to obtain: \[ \frac{x^2}{2} + \frac{y^2}{3} = 1 \] This represents an ellipse in standard form with \( a^2 = 3 \) and \( b^2 = 2 \).

Step 2: Determine the major axis and coordinates.
The major axis length is \( 2a = 2\sqrt{3} \), and the vertices are at \( (0, \pm\sqrt{3}) \), so the correct answer is 1. \( 2\sqrt{2}, (0, \pm\sqrt{3}) \).