Question:
If the length of the major axis of an ellipse is thrice the length of the minor axis, then its eccentricity is equal to:
If the length of the major axis of an ellipse is thrice the length of the minor axis, then its eccentricity is equal to:
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Always express everything in terms of one variable.
Updated On: Apr 30, 2026
- \(\frac{2\sqrt{2}}{3} \)
- \(\frac{\sqrt{2}}{\sqrt{3}} \)
- \(\frac{1}{2} \)
- \(\frac{1}{\sqrt{2}} \)
- \(\frac{1}{2\sqrt{2}} \)
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The Correct Option is A
Solution and Explanation
Concept:
Ellipse relations:
\[
e = \frac{c}{a}, \quad c^2 = a^2 - b^2
\]
Step 1: Use given condition.
\[ 2a = 3(2b) \Rightarrow a = 3b \]
Step 2: Find eccentricity.
\[ c^2 = a^2 - b^2 = 9b^2 - b^2 = 8b^2 \] \[ c = 2\sqrt{2}b \] \[ e = \frac{c}{a} = \frac{2\sqrt{2}b}{3b} = \frac{2\sqrt{2}}{3} \]
Step 1: Use given condition.
\[ 2a = 3(2b) \Rightarrow a = 3b \]
Step 2: Find eccentricity.
\[ c^2 = a^2 - b^2 = 9b^2 - b^2 = 8b^2 \] \[ c = 2\sqrt{2}b \] \[ e = \frac{c}{a} = \frac{2\sqrt{2}b}{3b} = \frac{2\sqrt{2}}{3} \]
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