One of the
conic sections. In this
vein, its relatives are the
circle, the
ellipse and the
hyperbola. The generating
equation for a parabola
centered on the
origin is
y=ax2 for some
constant a. Other parabolic shapes can be generated with the equation
y=ax2n for some
constant a in the
real numbers and n in the
natural numbers.
The defining characteristic of a parabola is that each point is
equidistant from a point P and a
line L which does not pass through the point. To this end, each
point of a parabola is the center of a circle whose edge passes through the point P and touches the
line L. The idea of a circle comes into play because each point on the edge of a circle is equidistant from the center.
Uses:
mirrors in
telescopes or
headlights;
parabolic surfaces in
sound reflection;
etc. The
reason for these uses is that
radiated energy from the
focus of the parabola always ends up travelling in one direction. For
example, a headlight contains a
light source and a parabolic
mirror. When any particular light beam from the light source hits the sides of the
parabolic mirror, that beam is then directed in one direction (and only that direction, ignoring
diffusion), parallel to all the other light beams which have
bounced off the mirror. This is a partial
laser effect; it is not complete since most light beams are significantly diffused at production, and few mirrors are "
perfect".