In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x 2 − y 2 = 1. {\displaystyle x^{2}-y^{2}=1...

In mathematics, a hyperbola (/haɪˈpɜːrbələ/ ; pl. hyperbolas or hyperbolae /-liː/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in...

Pythagorean trigonometric identity Riemannian circle Radian Unit disk Unit sphere Unit hyperbola Unit square Turn (angle) z-transform Smith chart For further...

when this hyperbola is re-scaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola. A hyperbolic...

{arsinh} x)=x.} Hyperbolic angle measure is the length of an arc of a unit hyperbola x 2 − y 2 = 1 {\displaystyle x^{2}-y^{2}=1} as measured in the Lorentzian...

through (a, 0) and (−a, 0). The case a = 1 is called the unit hyperbola. The conjugate hyperbola is given by { z : ‖ z ‖ 2 = − a 2 } {\displaystyle \left\{z:\lVert...

Quadrant I of the Cartesian plane. The hyperbolic angle parametrises the unit hyperbola, which has hyperbolic functions as coordinates. In mathematics, hyperbolic...

functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t,...

the unit hyperbola, since ( c / a ) 2 − ( b / a ) 2 = 1 , {\displaystyle (c/a)^{2}-(b/a)^{2}=1,} satisfying the equation for the unit hyperbola. The...

x^{2}-y^{2}} , when set equal to one, produces the unit hyperbola, which plays the role of the "unit circle" in the plane of split-complex numbers. Similarly...