If `(2, 0)` is the vertex and the `y -` axis is the directrix of a parabola, then where is its focus?

Options

A. `(0, 0)`
B. `(-2, 0)`
C. `(4, 0)`
D. `(-4, 0)`

Answer

To find the focus of the parabola given that the vertex is at (2, 0) and the y-axis is the directrix, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Vertex and Directrix:**
- The vertex of the parabola is given as \( V(2, 0) \).
- The directrix is the y-axis, which can be represented as the line \( x = 0 \).

**Hint:** The vertex is the midpoint between the focus and the directrix.

2. **Determine the Distance from the Vertex to the Directrix:**
- The distance from the vertex \( (2, 0) \) to the directrix (y-axis) is the x-coordinate of the vertex, which is \( 2 \) units.

**Hint:** The distance from the vertex to the directrix is equal to the distance from the vertex to the focus.

3. **Calculate the Focus:**
- Since the vertex is at \( (2, 0) \) and the distance to the directrix is \( 2 \), the focus will be located \( 2 \) units to the right of the vertex (since the directrix is on the left).
- Therefore, the x-coordinate of the focus will be \( 2 + 2 = 4 \).
- The y-coordinate of the focus remains the same as the vertex, which is \( 0 \).

**Hint:** The focus will have the same y-coordinate as the vertex if the parabola opens horizontally.

4. **Final Coordinates of the Focus:**
- Thus, the coordinates of the focus are \( F(4, 0) \).

### Conclusion:
The focus of the parabola is at the point \( (4, 0) \).

**Final Answer:** The focus is at \( (4, 0) \).