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Question
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.
Options
`8/3`
`2/3`
`4/3`
`5/3`
MCQ
Fill in the Blanks
Solution
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is `underlinebb(8/3)`.
Explanation:
Perpendicular distance of directrix from
focus = `a/e - ae` = 4
`\implies a(2 - 1/2)` = 4
`\implies a = 8/3`
∴ Semi major axis = `8/3`
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Conic Sections - Ellipse
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