The given parabola is in the form x² = 4py, where p is the distance from the vertex to the focus, and also from the vertex to the directrix. From the equation x² = 28y, we can see that 4p = 28, which means p = 7.
Vertex: The vertex of the parabola is at the origin (0, 0). This is because the standard form x² = 4py opens upwards, and in this case, there are no horizontal or vertical shifts.
Focus: The focus of the parabola can be found by moving a distance p from the vertex along the axis of symmetry. Since p = 7, the coordinates of the focus will be (0, 7).
Directrix: The directrix of a parabola is a horizontal line located a distance p from the vertex in the opposite direction of the focus. This means the directrix will be located at y = -7.
Focal Width: The focal width (also known as the latus rectum) is the length of the line segment that passes through the focus and is perpendicular to the axis of symmetry. It is equal to 4p. Since p = 7, the focal width will be 4 * 7 = 28.
Summary:
- Vertex: (0, 0)
- Focus: (0, 7)
- Directrix: y = -7
- Focal Width: 28