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QJEEM08Ma37e5: JEE Main 2008 Mathematics - Class 11 JEEM08Ma37e5 Solution: A focus of an ellipse is at the origin. The directrix is the…

A focus of an ellipse is at the origin. The directrix is the line x=4x=4 and the eccentricity is 12{{1 \over 2}} . Then the length of the semi-major axis is :

Multiple Choice Options

  • A 83{{8 \over 3}}
  • B 23{{2 \over 3}}
  • C 43{{4 \over 3}}
  • D 53{{5 \over 3}}

Step-by-Step Verified Solution

AIEEE 2008 Mathematics - Ellipse Question 89 English Explanation

Perpendicular distance of directrix from focus

=ae−ae=4= {a \over e} - ae = 4

⇒a(2−12)=4\Rightarrow a\left( {2 - {1 \over 2}} \right) = 4

⇒a=83\Rightarrow a = {8 \over 3}

∴\therefore Semi major axis =8/3=8/3

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