In mathematics, hyperbola is a conic curve, defined as two halves of a right-angled conic surface with intersecting planes. It can also be defined as the trajectory of a point whose distance difference from a point to two fixed points is constant. This fixed distance difference is twice that of A, where A is the distance from the center of hyperbola to the vertex of the nearest branch of hyperbola.
Algebraically speaking, hyperbola is a curve defined by the following formula on Cartesian plane, so all the coefficients here are real numbers, and the point pair (x, y) defined on hyperbola has more than one solution. Note that the image of two reciprocal variables on Cartesian coordinate plane is a hyperbola.
Numerical characteristics of eccentricity;
As far as ellipse is concerned, eccentricity is the degree to control its flatness. When e tends to 1, the ellipse is "long", and when e tends to 0, the ellipse is very round. On the other hand, for hyperbola, the square e is 1+(a/b), so it can be seen that e controls the slope of hyperbolic asymptote, that is, the concavity and convexity of hyperbola. When e tends to 1, ellipse and parabola tend to be a straight line.
Conic curves were discovered in the study of "cubic problems". At that time, people could only draw circles, and they described them by the size of eccentricity. Throughout the history of mathematical development, eccentricity was first introduced to describe the shape of planetary orbits in the solar system, that is, the deviation between elliptical orbits and ideal rings.