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Learn how to derive and use the standard equation of a parabola, y 2 = 4ax, and its properties. Find the vertex, focus, directrix, axis of symmetry, and latus rectum of different types of parabolas.
Learn how to derive the equation of a parabola in standard form from the definition of a parabola as the locus of points equidistant from a focus and a directrix. See the focal distance, vertex, and directrix of a parabola and how to graph them.
Learn what a parabola is, how to draw it, and how to write its equation in different forms. Find out how to use parabolas for reflectors, dishes, and projectiles.
Learn how to write and graph parabola equations in different forms, such as vertex, conics, and standard. Find out the keywords, properties, and applications of parabolas in geometry and physics.
28 Σεπ 2024 · The equation of a parabola depends on its orientation, the position of its vertex, and whether it is centered at the origin or elsewhere. Standard Form. A horizontal parabola is a parabola that opens sideways, either to the left or to the right. y 2 = 4ax. Here, The equation of the axis of symmetry is y = 0. The equation of directrix is x = -a.
6 Οκτ 2021 · Start by writing the equation of the parabola in standard form. The standard form that applies to the given equation is \({(x−h)}^2=4p(y−k)\). Thus, the axis of symmetry is parallel to the \(y\)-axis.
Learn what a parabola is, how to write its equation in standard or vertex form, and how to find its focus, directrix, axis of symmetry, and zeros. See graphs and examples of parabolas with different orientations and focal lengths.
