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Thus, in an xy-coordinate system the graph of a function :, >, with equation =, >, is a rectangular hyperbola entirely in the first and third quadrants with the coordinate axes as asymptotes , the line y = x {\displaystyle y=x} as major axis ,
Each hyperbola is defined by = / and = / (with =, =) in equation . Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity . It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola , as can be seen when graphed on a Minkowski diagram ...
A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).
The unit hyperbola is blue, its conjugate is green, and the asymptotes are red. In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation = In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length
A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1, or the corresponding region 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.
In general, inversion with respect to an arbitrary curve may produce an algebraic curve with proportionally larger degree. Specifically, if C is p -circular of degree n , and if the center of inversion is a singularity of order q on C , then the inverse curve will be an ( n − p − q ) -circular curve of degree 2 n − 2 p − q and the ...
a line, if the plane is parallel to the z-axis, and has an equation of the form + =, a parabola, if the plane is parallel to the z-axis, and the section is not a line, a pair of intersecting lines, if the plane is a tangent plane, a hyperbola, otherwise. STL hyperbolic paraboloid model
Feuerbach Hyperbola. In geometry, the Feuerbach hyperbola is a rectangular hyperbola passing through important triangle centers such as the Orthocenter, Gergonne point, Nagel point and Schiffler point. The center of the hyperbola is the Feuerbach point, the point of tangency of the incircle and the nine-point circle. [1]