Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directrix: x=-12

The standard form of a parabola that opens horizontally is given by the equation (y - k)² = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. This form allows for easy identification of the parabola's orientation and key features, such as the focus and directrix.

In the context of parabolas, the focus is a fixed point from which distances to points on the parabola are measured, while the directrix is a line that is perpendicular to the axis of symmetry. The parabola is defined as the set of points equidistant from the focus and the directrix, which is crucial for determining its equation.

The vertex of a parabola is the point where it changes direction and is located midway between the focus and the directrix. For a parabola that opens horizontally, the vertex can be calculated as the midpoint of the focus and the directrix, which is essential for writing the standard form of the parabola's equation.