Hyperbola refers to the locus of a point whose absolute value of the distance difference between a plane and two fixed points is constant, and can also be defined as the locus of a point whose distance ratio from a fixed point to a fixed line is constant greater than 1. Hyperbola is a kind of conic curve, that is, the intersection of a conical surface and a plane parallel to the central axis.
Extended data
Each branch of a hyperbola has two straighter (lower curvature) arms that extend further from the center of the hyperbola. Diagonally opposite arms, one for each branch, tend to have the same line, which is called the asymptote of these two arms.
So there are two asymptotes, and their intersection points are located in the symmetrical center of hyperbola, which can be regarded as the mirror image points of each branch reflecting to form the other branch. When the curve {\ displaystylef (x) =1/x} f (x) =1/x, the asymptote has two coordinate axes.
Hyperbola * * * enjoys many analytical properties of ellipse, such as eccentricity, focus and pattern. Many other mathematical objects are derived from hyperbola, such as hyperbolic paraboloid (saddle surface) and hyperboloid ("trash can").
Hyperbolic geometry (Lobachevsky's famous non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc. ) and gyro vector space (geometry proposed for relativity and quantum mechanics, not Euclid).
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