Question

The eccentricity of the ellipse \( 9x^{2} + 5y^{2} = 45 \) is:

• A. 3/2
• B. 2/3
• C. 1/3
• D. 1/2

Hint:

Eccentricity of an ellipse is always less than 1.

Answer 1

The Correct Option is B

Step 1: Concept
Standardize the equation to $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Eccentricity $e = \sqrt{1 - \frac{(\text{smaller semi-axis})^2}{(\text{larger semi-axis})^2}}$.
Step 2: Analysis
$\frac{x^{2}}{5} + \frac{y^{2}}{9} = 1$. Here $b^{2}=9$ (major axis) and $a^{2}=5$ (minor axis). $e = \sqrt{1 - 5/9} = \sqrt{4/9}$.
Step 3: Conclusion
$e = 2/3$.
Final Answer: (B)