2. (Geom.) A point so related to a conic section and certain
straight line called the directrix that the ratio of the
distace between any point of the curve and the focus to
the distance of the same point from the directrix is
constant.
Note: Thus, in the ellipse FGHKLM, A is the focus and CD the
directrix, when the ratios FA:FE, GA:GD, MA:MC, etc.,
are all equal. So in the hyperbola, A is the focus and
CD the directrix when the ratio HA:HK is constant for
all points of the curve; and in the parabola, A is the
focus and CD the directrix when the ratio BA:BC is
constant. In the ellipse this ratio is less than unity,
in the parabola equal to unity, and in the hyperbola
greater than unity. The ellipse and hyperbola have each
two foci, and two corresponding directrixes, and the
parabola has one focus and one directrix. In the
ellipse the sum of the two lines from any point of the
curve to the two foci is constant; that is:
AG+GB=AH+HB; and in the hyperbola the difference of the
corresponding lines is constant. The diameter which
passes through the foci of the ellipse is the major
axis. The diameter which being produced passes through
the foci of the hyperbola is the transverse axis. The
middle point of the major or the transverse axis is the
center of the curve. Certain other curves, as the
lemniscate and the Cartesian ovals, have points called
foci, possessing properties similar to those of the
foci of conic sections. In an ellipse, rays of light
coming from one focus, and reflected from the curve,
proceed in lines directed toward the other; in an
hyperbola, in lines directed from the other; in a
parabola, rays from the focus, after reflection at the
curve, proceed in lines parallel to the axis. Thus rays
from A in the ellipse are reflected to B; rays from A
in the hyperbola are reflected toward L and M away from
B.
3. A central point; a point of concentration.
{Aplanatic focus}. (Opt.) See under {Aplanatic}.
{Conjugate focus} (Opt.), the focus for rays which have a
sensible divergence, as from a near object; -- so called
because the positions of the object and its image are
interchangeable.
{Focus tube} (Phys.), a vacuum tube for R[oe]ntgen rays in
which the cathode rays are focused upon the anticathode,
for intensifying the effect.
{Principal, or Solar}, {focus} (Opt.), the focus for parallel
rays.