Parabola with axis parallel to y -axis; p is the semi-latus rectum In Cartesian coordinates, if the vertex is the origin and the directrix has the equation , then, by examining the case , the focus is on the positive -axis, with , where is the focal length. The above geometric characterization implies that a point is on the parabola if and only if Solving for ...
parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone—that is, the cone’s surface.
This curve is a parabola (Figure 12 3 2). Figure 12 3 2: Parabola Like the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points (x, y) in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point and a fixed line. Its general equation is of the form y^2 = 4ax (if it opens left/right) or of the form x^2 = 4ay (if it opens up/down)
When we kick a soccer ball (or shoot an arrow, fire a missile or throw a stone) it arcs up into the air and comes down again ...
Parabolas are a particular type of geometric curve, modelled by quadratic equations. Parabolas are fundamental to satellite dishes and headlights.