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Year_11_2U_Hyperbola.pdf (754 × 566 pixels, file size: 846 KB, MIME type: application/pdf, 10 pages) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
Download as PDF; Printable version ... A hyperbola is an open curve with two ... the eccentricity can be found using the formula in Conic section#Eccentricity in ...
Download as PDF; Printable version; ... This formula can be derived from the formulas about ... The lines in this model are represented as branches of a hyperbola. [35]
A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...
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.
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 curve represents xy = 1. A hyperbolic angle has magnitude equal to the area of the corresponding hyperbolic sector, which is in standard position if a = 1. In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... In all formulas the constant a is assumed to be nonzero, ...