What is Hyperbola?
[[File:Hyperbola (PSF).svg|right|thumb|150px|A hyperbola is the intersection between both halves of a double cone and a plane.]] [[File:Cathedral Brasilia Niemeyer.JPG|thumb|[[Brasilia Cathedral]]: The white structures are hyperbolas.]] A '''hyperbola''' is a type of [[conic section]]. Like the other three types of conic sections - [[parabola]]s, [[ellipse]]s, and [[circle]]s - it is a [[curve]] formed by the intersection of a [[cone]] and a [[plane (mathematics)|plane]]. A hyperbola is created when the plane intersects both halves of a double cone, creating two curves that look exactly like each other, but open in opposite directions. This occurs when the [[angle]] between the [[axis (mathematics)|axis]] of the cone and the plane is less than the angle between a line on the side of the cone and the plane. Hyperbolas can be found in many places in nature. For example, an object in open orbit around another object - where it never returns - can move in the shape of a hyperbola. On a [[sundial]], the path followed by the tip of the shadow over time is a hyperbola. One of the most well-known hyperbolas is the [[graph]] of the equation <math>f(x) = 1/x</math>. == Definitions and equations == [[File:Hyperbola properties.svg|right|frame|Graph of a hyperbola (red curves). The asymptotes are shown as blue dashed lines. The center is labeled ''C'' and the two vertices are located at ''-a'' and ''a''. The foci are labeled ''F<sub>1</sub>'' and ''F<sub>2</sub>''.]] The two disconnected curves that make up a hyperbola are called '''arms''' or '''branches'''. The two points where the branches are closest together are called the [[vertex|vertices]]. The line between these two points is called the ''transverse axis'' or ''major axis''. The [[midpoint]] of the transverse axis is the ''center'' of the hyperbola. At large distances from the center, the branches of the hyperbola approach two straight lines. These two lines are called the [[asymptote]]s. As the distance from the center increases, the hyperbola gets closer and c