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`

Explanation

To solve the problem step by step, we will use the properties of an ellipse, focusing on the relationship between the focus, directrix, eccentricity, and the semi-major axis.

### Step 1: Understand the given information
- Focus (F) of the ellipse is at the origin (0, 0).
- Directrix (D) is the line \( x = 4 \).
- Eccentricity (e) is given as \( \frac{1}{2} \).

### Step 2: Use the relationship between the semi-major axis (A), eccentricity (e), and directrix
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