Here are the essential concepts you must grasp in order to answer the question correctly.
Parabola Definition
A parabola is a symmetric curve formed by the set of all points that are equidistant from a fixed point called the focus and a fixed line known as the directrix. The orientation of the parabola depends on the position of the focus relative to the directrix, which can be vertical or horizontal.
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Standard Form of a Parabola
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 or directrix. This form allows for easy identification of the vertex and the direction in which the parabola opens.
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Parabolas as Conic Sections
Finding the Vertex
The vertex of a parabola is the midpoint between the focus and the directrix. In this case, with the focus at (-5, 0) and the directrix at x = 5, the vertex can be calculated as the average of the x-coordinates of the focus and the directrix, resulting in the vertex being at (-5, 0). This is crucial for writing the equation in standard form.
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