Hyperbolas

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A ray of light projected from one focus and reflected in a normal to the hyperbola will reflect to the other focus.
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Given two foci, the hyperbola can be defined as the locus of points, the difference of whose distance to the foci is constant.
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Given a point (the focus) and a line (the directrix), we examine the locus of the points whose distance from the focus is k times the distance from th...
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We see that if we have the hyperbola and the conjugate hyperbola, then the points at parameter locations t on one hyperbola and –t on the other lie on...
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We see the coordinates of the point at parametric location t on the hyperbola.
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For the Hyperbola, we see that each axis intersection depends on only one parameter of the curve, the x-axis on a, the y-axis on b:
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We look at the locus of the intersections of the tangents at the end of the diameter and the focal chord through a point. This locus is a circle with ...
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The equivalent to defining an ellipse with the equation (x^2/a^2)+(y^2/b^2)=1 , is to define a hyperbola with equation (x^2/a^2)-(y^2/b^2)=1 . We al...
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