The hyperbola. It is a conical section, an open two-branch curve obtained by cutting a straight cone by an plane oblique to the axis of symmetry – with an angle less than that of the generatrix with respect to the axis of revolution.
Summary
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- 1 Story
- 2 Definition
- 1 The general equation of the hyperbola.
- 3 Applications
- 4 See also
- 5 Sources
History
According to tradition, the conic sections were discovered by Menecmo, in his study of the problem of cube duplication, where he demonstrates the existence of a solution by cutting a parabola with a hyperbola, which is later confirmed by Proclus and Eratosthenes .
Definition
The hyperbola is the locus of points on a plane such that the modulus of the difference in their distances to two fixed points on the same plane, called foci, is a constant less than the distance between the foci.
The general equation of the hyperbola.
The center hyperbola at the origin of coordinates and semi-axes a and b with the main axis on the x axis has the equation :
x 2 / a 2 -y 2 / b 2 = 1
Applications
Hyperbolas have a practical use in the field of optics and astronomy : two massive bodies that interact according to the law of universal gravitation, their trajectories describe conic sections if their center of mass is considered at rest. If they are relatively close they will describe ellipses , if they are too far away they will describe hyperbolas or parabolas . They are also important in the construction of bridges, aerodynamics and in their industrial application, since they allow them to be repeated by mechanical means with great accuracy, achieving perfect surfaces, shapes and curves.
