What is the vertex of the parabola. assume p> 0

The emphasis and the equidistant from the vertex but on opposite sides. As the focus is at (0, p) and the directrix has the equation y = -p then its nearest point to the vertex is at (0,-p) and thus the vertex is at the origin (0,0). The parabola is balanced about the y axis. The normal calculation for a parabola opening up with its vertex at the origin is, x² = 4cy where c is the distance from the vertex to the focus. Reorganizing the original equation gives: - y = ¼px²: x² = 4(1/p) y . . . but this would mean that the distance from the vertex to the focus is (1/p).  So the parabola equation must be y = ¼(1/p) x² or (1/4p) x² and thus x² = 4py

.mp4 files, because, video

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step-by-step explanation: