Step 1: Understanding the Concept:
This question deals with the fundamental properties of a parabola: the vertex, focus, and directrix. The vertex is always the midpoint between the focus and the directrix along the axis of symmetry.
Step 2: Key Formula or Approach:
1. The axis of the parabola is perpendicular to the directrix and passes through the vertex.
2. The distance from the vertex to the focus is equal to the distance from the vertex to the directrix. Let this distance be 'a'.
3. The focus lies on the axis of symmetry, on the opposite side of the vertex from the directrix.
Step 3: Detailed Explanation:
We are given:
Vertex V = $(2, 0)$.
Directrix is the y-axis, which is the line $x = 0$.
First, determine the axis of symmetry. Since the directrix is a vertical line ($x=0$), the axis of symmetry must be a horizontal line passing through the vertex. The equation of the axis of symmetry is therefore $y = 0$ (the x-axis).
The focus must lie on this axis. So, the focus will have coordinates $(f, 0)$ for some value $f$.
The distance 'a' from the vertex to the directrix is the horizontal distance between the point $(2,0)$ and the line $x=0$.
\[ a = |2 - 0| = 2 \]
The parabola opens away from the directrix. Since the directrix is to the left of the vertex, the parabola opens to the right.
The focus is also at a distance 'a' from the vertex, along the axis of symmetry, in the direction the parabola opens.
So, the x-coordinate of the focus will be the x-coordinate of the vertex plus 'a'.
\[ x_{focus} = x_{vertex} + a = 2 + 2 = 4 \]
The y-coordinate of the focus is the same as the vertex, which is 0.
Therefore, the focus is at $(4, 0)$.
Step 4: Final Answer:
The coordinates of the focus are (4, 0). Therefore, option (C) is correct.