The length of major axis and coordinate of vertices for the ellipse \( 3x^2 + 2y^2 = 6 \) respectively are:
Show Hint
- \( 2\sqrt{2}, (0, \pm\sqrt{3}) \)
- \( 2\sqrt{3}, (0, \pm\sqrt{3}) \)
- \( 2\sqrt{2}, (\pm\sqrt{3}, 0) \)
- \( 2\sqrt{3}, (\pm\sqrt{3}, 0) \)
The Correct Option is A
Solution and Explanation
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. \( 2\sqrt{2}, (0, \pm\sqrt{3}) \).
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