Hyperbola
Hyperbola
!A hyperbola is an open curve with two branches, the intersection of a [plane) with both halves of a double cone). The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.](//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Hyperbola%28PSF%29.svg/250px-Hyperbola%28PSF%29.svg.png)
Hyperbola
Besides being a conic section, a hyperbola can arise as the locus) of points whose difference of distances to two fixed foci) is constant, as a curve for each point of which the rays to two fixed foci are reflections) across the tangent line at that point, or as the solution of certain bivariate quadratic equations such as the reciprocal relationship ${\displaystyle xy=1.}$ In practical applications, a hyperbola can arise as the path followed by the shadow of the tip of a sundial's gnomon, the shape of an open orbit such as that of a celestial object exceeding the escape velocity of the nearest gravitational body, or the scattering trajectory of a subatomic particle, among others.
Hyperbola
Each branch) of the hyperbola has two arms which become straighter (lower curvature) further out from the center of the hyperbola. Diagonally opposite arms, one from each branch, tend in the limit to a common line, called the asymptote of those two arms. So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve ${\displaystyle y(x)=1/x}$ the asymptotes are the two coordinate axes.
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