Parabola.
Publié le 06/12/2021
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Parabola.
Parabola, two-dimensional curve that matches the path a tossed object such as a ball follows. Each point on the curve is equally distant from a fixed point, called the
focus, and a fixed straight line, known as the directrix. The very tip of a parabola is called the vertex.
Parabolas are important in astronomy and physical science. An object in space follows a parabolic orbit as it swings around a central mass if the object has just barely
enough momentum to escape from the gravity of the central mass forever. An asteroid that followed such a path around the Sun would fly off into interstellar space,
never to return. Parabolic mirrors (reflectors that have the shape of a parabola) reflect rays of light in parallel lines from a light source located at the mirror's focus.
Such reflectors are used in automobile headlights and in searchlights. Parabolic mirrors also bring parallel rays of light to a focus. This type of reflector is therefore
valuable in astronomical telescopes. Parabolic reflectors also are used as antennas in radio astronomy and radar.
Any parabola is symmetrical about a line that passes through the focus and is perpendicular to the directrix, meaning that the half-parabolas on each side of the line are
mirror images of one another. A parabola can be drawn on xy axes by graphing its equation. For a parabola with a horizontal directrix and a vertex at (h, k), the
equation is (x - h )2 = 2p (y - k), in which p is the distance between the focus and the directrix. Conversely, the equation of a parabola with a vertical directrix is (y - k)2
= 2p (x - h ).
Parabolas are one of the conic section curves formed by the intersection of a right circular cone and a plane. A parabola is formed when the plane is parallel to a straight
line drawn on the slanting surface of the cone from the tip of the cone to its base.
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
Parabola.
Parabola, two-dimensional curve that matches the path a tossed object such as a ball follows. Each point on the curve is equally distant from a fixed point, called the
focus, and a fixed straight line, known as the directrix. The very tip of a parabola is called the vertex.
Parabolas are important in astronomy and physical science. An object in space follows a parabolic orbit as it swings around a central mass if the object has just barely
enough momentum to escape from the gravity of the central mass forever. An asteroid that followed such a path around the Sun would fly off into interstellar space,
never to return. Parabolic mirrors (reflectors that have the shape of a parabola) reflect rays of light in parallel lines from a light source located at the mirror's focus.
Such reflectors are used in automobile headlights and in searchlights. Parabolic mirrors also bring parallel rays of light to a focus. This type of reflector is therefore
valuable in astronomical telescopes. Parabolic reflectors also are used as antennas in radio astronomy and radar.
Any parabola is symmetrical about a line that passes through the focus and is perpendicular to the directrix, meaning that the half-parabolas on each side of the line are
mirror images of one another. A parabola can be drawn on xy axes by graphing its equation. For a parabola with a horizontal directrix and a vertex at (h, k), the
equation is (x - h )2 = 2p (y - k), in which p is the distance between the focus and the directrix. Conversely, the equation of a parabola with a vertical directrix is (y - k)2
= 2p (x - h ).
Parabolas are one of the conic section curves formed by the intersection of a right circular cone and a plane. A parabola is formed when the plane is parallel to a straight
line drawn on the slanting surface of the cone from the tip of the cone to its base.
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
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