1. The problem involves analyzing the parabola given by the equation $y^2 = 8x$. 2. We identify the parabola as one that opens to the right because it is in the form $y^2 = 4ax$. 3. From the equation, we can find the parameter $a$ by comparing: $$4a = 8 \Rightarrow a = 2.$$ 4. The vertex of the parabola is at the origin $(0,0)$, which is the point where the parabola changes direction. 5. The focus of the parabola is given by the point $(a, 0) = (2, 0)$. 6. The directrix is the vertical line given by $x = -a = -2$; this line is the locus of points equidistant from the vertex but opposite the focus. 7. The key features of the parabola are: - Vertex: $(0,0)$ - Focus: $(2,0)$ - Directrix: $x = -2$ The problem is now fully analyzed and understood using standard parabola properties.