2. Mathematically, hyperbola (multiple hyperbola or hyperbola) is a smooth curve on a plane, which is defined by the equation of its geometric characteristics or the combination of its solutions. A hyperbola has two parts, called connected components or branches, which are mirror images of each other, similar to two infinite bows.
3. Hyperbola is one of the three conic curves formed by the intersection of plane and double cone. Other conical parts are parabolas and ellipses, and circles are special cases of ellipses. If the plane intersects the two halves of a double cone, but does not pass through the vertex of the cone, the conic curve is a hyperbola.
Each branch of hyperbola has two straighter (lower curvature) arms, which extend further from the center of 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.
5. Hyperbola * * * enjoys many analytic attributes of ellipse, such as eccentricity, focus, pattern, etc. Many other mathematical objects are derived from hyperbola, such as hyperbolic paraboloid, hyperbolic geometry, hyperbolic function, gyro vector space and so on.
6. Each branch of the hyperbola has two straighter (lower curvature) arms, which 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.