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Conic Sections Hyperbolas |
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Conic Axes Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the curve vertices of the conic.... |
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Equal Hyperbolas, Rolling of Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances between their foci O1 and O2, and d and e, are each equal to fg=hk, the... |
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Hyperbola One of the three species of conic sections is the hyperbola.... |
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Hyperbola Illustration showing a hyperbola as a curve formed by the intersection of the surface of a cone with a plane parallel to the axis of the cone.... |
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Hyperbola, Asymptotes of a Illustration showing the asymptotes of a hyperbola. The asymptotes will never meet the curve.... |
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Hyperbola, Auxiliary Circle and Illustration of a hyperbola and its auxiliary circle. "Any ordinate of a hyperbola is to the tangent from its foot to the auxiliary circle as b is to a."... |
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Hyperbola, Cone Intersected by a Plane to Form a Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola. ... |
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Hyperbola, Conic Section Illustration of a cone cut by a plane parallel to the axis of the cone and perpendicular to the vertical plane of projection. The curve made by the intersection of the plane and the cone is called a ... |
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Hyperbola, Conic Section Showing Illustration showing the definition of an hyperbola as a conic section. "The section of a right circular cone made by a plane that cuts both nappes of the cone is a hyperbola." A double right circula... |
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Hyperbola, Conic Section Showing Illustration showing the definition of a hyperbola as a conic section. ... |
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Hyperbola, Conic Section Showing Illustration showing the definition of an hyperbola as a conic section. A hyperbola is formed from a double right circular cone with a plane parallel to the axis cutting through the cones.... |
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Hyperbola, Conic Section Showing An illustration showing the intersection of a plane and a double cone. The cone is intersected by a plane parallel to the axis. Thus forming a Hyperbola.... |
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Hyperbola, Conjugate Axis of Illustration showing how the a hyperbola is symmetrical with respect to its conjugate axis.... |
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Hyperbola, Conjugate Diameters Any two conjugate diameters of an hyperbola are harmonic conjugates with regard to the asymptotes.... |
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Hyperbola, Construction of Illustration showing how a hyperbola con be constructed by points, having been given the foci and the constant difference 2a.... |
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Hyperbola, Construction Of An illustration showing how to construct a hyperbola by plotting. "Having given the transverse axis BC, vertexes Aa, and foci ff'. Set off any desired number of parts on the axis below the focus, an... |
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Hyperbola, Construction Of An illustration showing how to construct a hyperbola by a pencil and a string. "Having given the transverse axis BC, foci f' and f, and the vertexes A and a. Take a rule and fix it to a string at e;... |
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Hyperbola, Construction of a Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis (2a). ... |
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Hyperbola, Demonstration of Definition Illustration showing the definition of an hyperbola. "An hyperbola may be described by the continuous motion of a point, as follows: To one of the foci F' fasten one end of a rigid bar F'B so that i... |
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Hyperbola, Foci Distance of Illustration of a hyperbola with distances to foci drawn. "The difference of the distances of any point from the foci of an hyperbola is greater than or less than 2a, according as the point is on the... |
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Hyperbola, Line Bisecting Angle in Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola a line is drawn bisecting the angle between the focal radii, every point in this line except P... |
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Hyperbola, Point on a Illustration of a point on a hyperbola. "If d denotes the abscissa (x-coordinate) of a point of an hyperbola, r and r' its focal radii, then r = ed - a, and r' = ed + a."... |
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Hyperbola, Tangent to Illustration showing how to draw a tangent to an hyperbola from a given point P on the convex side of the hyperbola.... |
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Hyperbola, Tangent to a Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola and bisecting the internal angle between the focal radii is a tangent."... |
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Hyperbola, Tangent Triangles All triangles formed by a tangent and the asymptotes of an hyperbola are equal in area.... |
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