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• Jump to Conic Sections: Hyperbola .

• Tangents to Ellipse/Hyperbola .

• Rectangle Tangent to Ellipse/Hyperbola .

• Simple Harmonic Motion: Hyperbola.

• Relationship of the exercise metabolic hyperbola and the change in CO2 to the measured inhaled CO2 response.

• Construction for a Double Hyperbola.
• Double Hyperbola.

• Hyperbola.
• A special case of the hyperbola was first studied by Menaechmus. This special case was xy = ab where the asymptotes are at right angles and this particular form of the hyperbola is called a rectangular hyperbola. ...
• Euclid and Aristaeus wrote about the general hyperbola but only studied one branch of it while the hyperbola was given its present name by Apollonius who was the first to study the two branches of the hyperbola. ...
• The focus and directrix of a hyperbola were considered by Pappus. ...
• The pedal curve of a hyperbola with its focus as pedal point is a circle. The pedal of a rectangular hyperbola with its centre as pedal point is a lemniscate. ...
• The evolute of the hyperbola with equation given above is the Lamé curve (ax)2/3 - (by)2/3 = (a + b)2/3. From a point between the two branches of the evolute two normals can be drawn to the hyperbola but from a point beyond the evolute four normals can be drawn. ...
• If the centre of a rectangular hyperbola is taken as the centre of inversion, the rectangular hyperbola inverts to a lemniscate. If the vertex of a rectangular hyperbola is taken as the centre of inversion, the rectangular hyperbola inverts to a right strophoid. If the focus of a hyperbola is taken as the centre of inversion, the hyperbola inverts to a limacon. In this last case if the asymptotes of the hyperbola make an angle of /3 with the axis which cuts the hyperbola then it inverts to a Trisectrix of Maclaurin. ...
• uk/history/Curves/Hyperbola. ...

• The Hyperbola.
• Orthogonal hyperbola as a special hyperbola .
• Parametric equations of the hyperbola .
• The hyperbola and to functions .
• Tangent line in a point D of a hyperbola .
• The locus of all points D such that abs(|D,F| - |D,F'|) = 2a is a hyperbola.
• We see that a The points F and F' are called the foci of the hyperbola. D(x,y) is on the hyperbola |D,F| - |D,F'| = (+ or -) 2a _______________ _______________ | 2 2 | 2 2 \| (x - c) + y - \| (x + c) + y = (+ or -) 2a Squaring ________________________________ 2 2 2 2 | 2 2 2 2 2 (x - c) + y + (x + c) + y - 2 \| ((x + c) + y ) ((x - c) + y ) = 4a. ... 2 2 2 2 2 2 2 2 (c - a ) x - a y = a (c - a ) 2 2 2 Since a 2 2 2 2 2 2 b x - a y = a b 2 2 x y -- - -- = 1 (***) 2 2 a b This is the equation of the hyperbola.
• The intersection points of the hyperbola with the x-axis are A'(-a,0) and A(a,0). ...
• Orthogonal hyperbola as a special hyperbola .
• If a = b the equation becomes 2 2 2 x - y = a This hyperbola is called an orthogonal hyperbola. Parametric equations of the hyperbola .
• The simultaneous equations (1) and (2) are equivalent to a x = ------ cos(t) b sin(t) y = ------- cos(t) or to a cos(t) = - x a y sin(t) = --- b x This system has a solution for t if and only if 2 2 sin (t) + cos (t) = 1 a 2 a y 2 (-) + (---) = 1 x b x 2 2 2 2 2 2 a b + a y = b x 2 2 x y -- - -- = 1 2 2 a b Hence, the two associated lines constitute a curve and that curve is the hyperbola.
• We say that (1) and (2) are parametric equations of the hyperbola.
• The point D(a sec(t) , b tan(t)) is on the hyperbola for each t-value and with each point of the hyperbola corresponds a t-value. The hyperbola and to functions .

• How to:  Show a hyperbola  is Rectangular. ...
•  For example how to show that the new Hyperbola (that contains the Incenter, Orthocentre and the Gergonne point) is .
• Some Facts about |the Rectangular Hyperbola.
•   For a rectangular hyperbola this has length 2a.   For a rectangular hyperbola  a = b. ...
• For a rectangular hyperbola  for any point P on the hyperbola and for Focal points S and S' then S'P - SP = 2a. ...
•   Then this construction shows that the new hyperbola is rectangular. ...
•   The hyperbola changes but the construction remains invariant! A dynamic geometry verification of the proposition that the new hyperbola is rectangular. ...

• hyperbola.
• The hyper part in the hyperbola word is derived from the Greek word 'huper', what means to surpass a certain limit 1). This excess is reached while adapting the areas in the old Greek way, in the case of the hyperbola. ...
• Apollonius gave the hyperbola its name.
• Nowadays a more common definition of the hyperbola is as being the curve for which the difference between the distances to the foci remains constant.
• The hyperbola has two asymptotes, what can be used to describe saturation-growth2).
• orthogonal hyperbola, equilateral hyperbola. or rectangular hyperbola: the two asymptotes are perpendicular.
• degenerate hyperbola: the hyperbola has been degenerated to his asymptotes  .
• adjungated hyperbola: given a hyperbola a second one is added, with the same asymptotes, but axes switched. ...
• the hyperbola is the isoptic of the parabola .
• the hyperbola can be seen as a sinusoidal spiral .
• depending on the center of inversion and the form of the hyperbola, as polar inverse the following curves can be obtained: .
• a pedal (center) of the rectangular hyperbola is the lemniscate .
• The Greek Euklid and Aristaeus wrote about the general hyperbola, although they confined the curve to one branch. ...
• Where do we see the hyperbola in our world? Well, take a cistern, filled with water, and place two oscillators, with same frequency and amplitude. Then you see an extinction in the form of hyperbolas, as result of the constant difference in distance between the two foci (oscillators), on a hyperbola. Above that, we find the hyperbola in various branches of science as variables, that are inversely proportional related.

• Hyperbola .
• A hyperbola can be constructed using the following paper folding method. ... The creases in the paper will form a hyperbola. ...
• We can specify a particular point on the hyperbola by finding the intersection of the blue line with a line drawn through the red point and the center of the circle. Put another way, a hyperbola consists of the points whose distance from the center of the circle minus the distance to the point outside the circle is equal to plus or minus the radius of the given circle. ...
• As you drag the red point around the circle, the blue point traces out a hyperbola. ...

• Date Prev Date Next   Thread Prev Thread Next   Thread Index Date Index Author Index Re: Nautilus-list Fix for zombie pipe by hyperbola.
• Subject: Re: Nautilus-list Fix for zombie pipe by hyperbola .
• But I believe that hyperbola on HEAD is scheduled for demolition. ...
• Re: Nautilus-list Fix for zombie pipe by hyperbola .
• Nautilus-list Fix for zombie pipe by hyperbola .

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