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 semimajor axis is (1) `8/3` (2) `2/3` (3) `4/3` (4) `5/3`

Answer 1

`a/e - ae = 4`
`a(1- e^2)/e = 4`
`a((1-1/4)/(1/2)) = 4`
`a*(3/4)/(1/2) = 4`
`a = 4*1/2 *4/3 `
`a= 8/3`
option 1 is correct