Question

The eccentricity of the ellipse whose major axis is three times the minor axis is:

• A. \( \frac{\sqrt{2}}{3} \)
• B. \( \frac{\sqrt{3}}{2} \)
• C. \( \frac{2\sqrt{2}}{3} \)
• D. \( \frac{2}{\sqrt{3}} \)

Hint:

The eccentricity of an ellipse depends on the ratio of the major and minor axis lengths. For an ellipse where \( a = 3b \), use the formula \( e = \sqrt{1 - \frac{b^2}{a^2}} \) to calculate the eccentricity.

Answer 1

The Correct Option is C

Step 1: The formula for eccentricity \( e \) of an ellipse is given by: \[ e = \sqrt{1 - \frac{b^2}{a^2}}, \] where \( a \) is the length of the major axis and \( b \) is the length of the minor axis.
Step 2: Given that \( a = 3b \), we substitute into the formula and calculate the eccentricity to be \( e = \frac{2\sqrt{2}}{3} \).

Final Answer: \[ \boxed{\frac{2\sqrt{2}}{3}} \]