In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of …

一般的，双曲线（希腊语“Υπερβολία” [3]，字面意思是“超过”或“超出”）是定义为平面交截直角 圆锥 面的两半的一类 圆锥曲线。 它还可以定义为与两个固定的点（叫做 焦点）的距离差是 常数 的点的 轨迹。 这个固定的距离差是a的两倍，这里的a是从双曲线的中心到双曲线最近的分支的 顶点 的距离。 a还叫做双曲线的实半轴。 焦点位于贯穿轴上，它们的中间点叫做 中心，中心一般位于 原点 处。 在数学中，双曲线（多重双曲线或双曲线）是位于平面中的一种平滑曲线，由其几何特 …

在数学中，双曲线（英語： hyperbola ；希臘語： ὑπερβολή ，意思是超过、超出）是定义为平面交截直角圆锥面的两半的一类圆锥曲线。 它还可以定义为与两个固定的点（称为 焦点 ）的 距离 差是常数的点的 轨迹 。

A hyperbola, a type of smooth curve lying in a plane, has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. A hyperbola is a set of points whose difference of distances from two foci is a constant value.

A hyperbola looks like two infinite bows, called "branches". Looking at the left hand branch in this diagram: any point P is closer to F than to G by some constant amount

2024年11月29日 · Mathematically, a hyperbola is a type of conic section that results when a plane intersects both halves of a double right circular cone at an angle. This intersection of the plane and cone generates two unbounded curves that are mirror images. These curves, known as branches, together form the hyperbola.

2025年3月5日 · The hyperbola is the shape of an orbit of a body on an escape trajectory (i.e., a body with positive energy), such as some comets, about a fixed mass, such as the sun. The hyperbola can be constructed by connecting the free end of a rigid bar , where is a focus , and the other focus with a string .

A hyperbola is the set of all points \((x,y)\) in a plane such that the difference of the distances between \((x,y)\) and the foci is a positive constant. The standard form of a hyperbola can be used to locate its vertices and foci. See Example \(\PageIndex{1}\).

What is an hyperbola? An hyperbola is one of the conic sections. Its equation is similar to that of an ellipse, but with a subtraction sign in the middle. The graph of an hyperbola looks nothing like an ellipse. What does an hyperbola look like? An hyperbola looks sort of like two mirrored parabolas, with the

Geometrically, a hyperbola is the set of points contained in a 2D coordinate plane that forms an open curve such that the absolute difference between the distances of any point on the hyperbola and two fixed points (referred to as the foci) is constant; refer to the figure below.