HYPERBOLA, A Mbige/W/, that which has one of its infinite legs fidling, within an angle formed by the asymptotes, and the other falling without that angle.
TivPEatioLa, Apo//aaian, the common hyperbola, as derived from the cone. See HYPERBOLA.
Ily PERBOLA, Deficient, a curve having only one a_sy mpt ote, though two hyperbolie legs running out infinitely by the side of the asymptote. hut contrary ways.
llvemtuoi.A, Equilateral, has its asymptotes equal to each other.
Hymitaohas, Lyinite•, or HveHaum.As OF TIIE ulcnFR KINDS, are expressed or defined by general equations similar to that of the conic or cotninon Iy1 erliola, only ral exponents, instead of the particular numeral ones, hut so that the sum of those on one side of the question is equal to the sum of those on the other side. Such as a y "'+' = b xr" (d .r)", where x and y are the abscissa and ordinate to the axis or diameter of the curve ; or .r"' y° =
where the abscissa x is taken on one asymptote, and the or dinate ji parallel to the other.
11 YP El: )1,1C CONOI I), a solid formed by the revolu tion of an hyperbola about its axis ; it is otherwise called HYP ERBOLOID. which see.
VyrEauomc CURVE, the same as the hyperbola. To draw a tangent to any point in the hyperbolic curve, draw a semi-diameter to the given point, and find its conjugate ; then through the given point, draw a straight line. parallel to the conjugate diameter ; which line will be a tangent to the curve.
To find the focus of the hyperbolic curve, take the dis tance between the extremities of the transverse and conjugate axes, and apply it from the centre upon the axis, and the remote extremity of the distance gives the focus.