Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram, formed by the tangent lines to the ellipse at the four endpoints of the conjugate diameters.
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Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram, formed by the tangent lines to the ellipse at the four endpoints of the conjugate diameters.
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When " a " = " b " the ellipse is a circle and the conjugate diameters are perpendicular while the hyperbola is rectangular and the conjugate diameters are hyperbolic-orthogonal.
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When " a " = " b " the ellipse is a circle and the conjugate diameters are perpendicular while the hyperbola is rectangular and the conjugate diameters are hyperbolic-orthogonal.
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Students making drawings to accompany the exercises in George Salmon s " A Treatise on Conic Sections " ( 1900 ) at pages 165 71 ( on conjugate diameters ) will be making Minkowski diagrams.
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The two conjugate diameters d _ 1', and d _ 2'( blue ) are given, and the Methods of drawing an ellipse usually require the axes of the ellipse to be known.
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Each pair of conjugate diameters of an ellipse has a corresponding "'tangent parallelogram "', sometimes called a "'bounding parallelogram "'( skewed compared to a bounding rectangle ).
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If the conjugate diameters are standing perpendicular to each other ( = 90 ^ \ circ ), the axes of the ellipse are already found : In this case, they are identical to the given conjugate diameters.
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If the conjugate diameters are standing perpendicular to each other ( = 90 ^ \ circ ), the axes of the ellipse are already found : In this case, they are identical to the given conjugate diameters.
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The notion of hyperbolic orthogonality arose in analytic geometry in consideration of conjugate diameters of ellipses and hyperbolas . if " g " and " g " 2 represent the slopes of the conjugate diameters, then g g'=-\ frac { b ^ 2 } { a ^ 2 } in the case of an ellipse and g g'= \ frac { b ^ 2 } { a ^ 2 } in the case of a hyperbola.
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