[1] a = |AA'|/2 is called also the

[2] O is the middle of AA', the circle c centered at O, with radius a is called the

[3] Defining the

[4] b is called the

[5] Equation y

[6] The two lines defined by the equation x

The line orthogonal to x-axis at H(h,0) is called a

[5] The direction of the normal at X(x,y) is (x/a

[6] This implies that the symmetric F* of F with respect to the tangent XT is on XF' and the middle G of FF* is on the auxiliary circle with diameter AA'.

[7] By the symmetry of the hyperbola about its center follows that the other point G' of intersection of line FG with the auxiliary circle has also the property that the normal to FG at G' is a tangent to the hyperbola. This tangent coincides with the tangent at the symmetric point of X i.e. the point with coordinates (-x,-y).

[8] All properties of hyperbolas, discussed so far, have their twins for ellipses (see Ellipse.html ). Ellipses and hyperbolas are the two kinds of conics called collectively

Look at HyperbolaAsymptotics.html for the equation of the hyperbola with respect to its two (non-orthogonal in general) asymptotic lines.

AsymptoticTriangle.html

AsymptoticTriangleInv.html

ConicsMaclaurin.html

Ellipse.html

HyperbolaFromRectangular.html

HyperbolaAsymptotics.html

HyperbolaProperty.html

HyperbolaRectangular.html

HyperbolaWRAsymptotics.html

RectHyperbola.html

RectHypeRelation.html

RectHyperSimpleGeneration.html

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