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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Mathematics
Chapter
Ellipse

JEE Main 2008 · Mathematics · Ellipse

A focus of an ellipse is at the origin. The directrix is the line...

A focus of an ellipse is at the origin. The directrix is the line x=4x=4 and the eccentricity is 1/21 / 2. Then the length of the semi-major axis is

Options

  1. A83\frac{8}{3}
  2. B23\frac{2}{3}
  3. C43\frac{4}{3}
  4. D53\frac{5}{3}

Correct answer

A. 83\frac{8}{3}

Step-by-step solution

Major axis is along xx-axis. ae−ae=4a(2−12)=4a=83.\begin{aligned}& \frac{a}{e}-a e=4 \\ & a \left(2-\frac{1}{2}\right)=4 \\ & a=\frac{8}{3} . \end{aligned}
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