<p>If the length of the major axis of an ellipse is 3 times the length of its minor axis then eccentricity, $e = $ ?</p>
Step-by-Step Solution
Key Concept: Use the relationship between major and minor axes to express the eccentricity formula in terms of the given ratio.
<p><strong>Step 1:</strong> Let major axis length be $2a$ and minor axis length be $2b$.</p><p><strong>Step 2:</strong> Given: $2a = 3(2b)$, so $a = 3b$.</p><p><strong>Step 3:</strong> For an ellipse, $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{b^2}{9b^2}} = \sqrt{1 - \frac{1}{9}} = \sqrt{\frac{8}{9}} = \frac{2\sqrt{2}}{3}$.</p><p>∴ Answer is $r$ ($\frac{2\sqrt{2}}{3}$).</p>
Correct Answer: r