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 ______.

विकल्प

• `8/3`

• `2/3`

• `4/3`

• `5/3`

Answer 1

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`