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A focus of an ellipse is at the origin. ...

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

A

`4//3`

B

`5//3`

C

`8//3`

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the length of semi-major and semi - minor axes be a and b respectively.
We have,
Distance between focus and directrix = 4
`rArr a/e - ae = 4 rArr 3/2 a = 4 rArr a = 8/3`
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