Ellipse
Eccentricity
Grade None

Question:

<p>The distance between foci of an ellipse is 6 and the minor axis is 8. Find the eccentricity of the ellipse.</p>
<p>\(\dfrac{3}{5}\)</p>
<p>\(\dfrac{4}{5}\)</p>
<p>\(\dfrac{1}{2}\)</p>
<p>\(\dfrac{2}{3}\)</p>

Step-by-Step Solution

Key Concept: Use the fundamental relationship 2c = distance between foci and 2b = minor axis to find 'a', then apply e = c/a. The semi-major axis 'a' is found from the constraint a² = b² + c².
<p><strong>Step 1:</strong> Extract given information</p><p>Distance between foci = 2c = 6 → <strong>c = 3</strong></p><p>Minor axis = 2b = 8 → <strong>b = 4</strong></p><p><strong>Step 2:</strong> Find semi-major axis using a² = b² + c²</p><p>a² = 4² + 3² = 16 + 9 = 25</p><p><strong>a = 5</strong></p><p><strong>Step 3:</strong> Calculate eccentricity</p><p>e = c/a = 3/5 = <strong>0.6</strong></p><p>∴ Answer: A (e = 3/5 or 0.6)</p>
Correct Answer: A

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