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A parabola is a conic section generated by the intersection of a cone, and a plane tangent to the cone or parallel to some plane tangent to the cone. If the plane is itself tangent to the cone, one would obtain a degenerate parabola, a line. A parabola can also be defined as locus of points which are equi distant from a given point (the focus) and a given line (the directrix).1 Definitions and overview
In Cartesian coordinates, a parabola with an axis parallel to the y axis with vertex (h, k), focus (h, k + p), and directrix y = k - p has the equation
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A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolas are similar. A parabola can also be obtained as the limit of a sequence of ellipsesThe Ellipse is also an elliptical street immediately in front of the White House. In mathematics, an ellipse is a figure corresponding to a circle which has been stretched in one direction. This is an example of a conic section and can be defined as the l where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction.
A parabola has a single axis of reflective symmetrySymmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. The three main symmetri, which passes through its focus and is perpendicular to its directrix. The point of intersection of this axis and the parabola is called the vertex. A parabola spun about this axis in three dimensions traces out a shape known as a paraboloidIn mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: : (elliptic paraboloid), or : (hyperbolic paraboloid). Hyperbolic paraboloid. There are two kinds of paraboloid: elliptic and hyperbolic. The elli of revolution. See also parabolic reflectorA parabolic reflector (also known as a parabolic dish or a parabolic mirror is a reflective device formed in the shape of a paraboloid of revolution. Parabolic reflectors can either collect or distribute energy such as light, sound, or radio waves. The pa.
A particle or body in motion under the influence of a uniform gravitational field (for instance, a baseball flying through the air, neglecting air frictionIn physics, friction is the resistive force that occurs when two surfaces travel along each other when forced together. It causes physical deformation and heat buildup. The frictional force is a function of the force pressing the surfaces together and the) follows a parabolic trajectory.
In real-world cases, the trajectory of a body is more likely to be elliptical (if it lacks escape velocityFor the video game title, see Escape Velocity (computer game). In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinite) or hyperbolic (if it has sufficient energyThis article is about the scientific concept. Energy use by humans is discussed in other articles''. Energy generally and qualitatively speaking, is the property (or the quantity of the property) of doing things or supplying power. The expressions energy to escape). For the trajectories of small bodies close to a massive body, the gravitational field is considered close enough to uniform to approximate a parabolic trajectory.
The parabola is an inverse transform of a cardioid.
