The hyperbola is the locus of points whose difference distances to other 2 fixed (called foci F1, F2) is constant and equal to the long axis V1, V2.
In the picture you can see that the distance of a point F2 (blue) minus the distance of F1 at that point (in green) is equal to V1-V2.
points are taken to build (from F1 to infinity and infinity to F2), for example from A to V1 and made her a bow with center F1. Then you take the distance from A to V2 and made an arc centered at F2. The intersection of the 2 arches is a point on the hyperbola.
can draw a branch by hyperbolic cone section of a dihedral system: the vertical plane cutting the cone with vertex V determines the branch of hyperbola. To calculate m we a vertical plane through the center of the cone, it cuts the circumference of the cone base in P1, point P2 project to the sum obtained on the ground line. The plane cut at T m the plane to at this point until we make a vertical cut in G. P2-V The other points are determined the same way. To determine the vertex E is a circle with center O is tangent to the plane, it intersects the ground line in Z. By Z is a vertical until it intersects the generatrix of the cone shape of H and by this point a short horizontal VO in E.
The intersection of a set of equidistant concentric circles are hyperbolic curves.
Given any 2 vertices of a hyperbola AB, construct a square with vertex at A and divide the sides into equal parts as provided in the figure. From B draw a radiation passing through points 1, 2, 3. For points across the square to make other radiation A.
The intersection of two radiations are the points of the curve.
The points to take to build the hyperbola should be, as is the Ellipse, between the two foci. The difference is that in the ellipse are points within the segment between two points, while in the hyperbola the chosen points ranging from a focus to infinity and from infinity to the other focus. Keeping
that every line has a point at infinity, it follows that the hyperbola, like the parable has a single point at infinity, as it pertains to the same curve and is located on the same line, albeit in homology we have that when the boundary line cuts the circle in two points, its counterpart must have given these two points at infinity.
To calculate the asymptotes or tangents to the hyperbola at infinity do a circle c with center O and O-F1 radio. At the intersection of the vertical by V1-V2 and circumference c we have 4 points which together with O define the asymptotes of the hyperbola.
A numerical example we have with drawing the hyperbola: From V1 to a point measuring 28.69, centered at F2 is an arc with that measure. V2
From that point is 13.6, with center in F1 is another arch with that as at the intersection with the anterior arch have a point on the hyperbola. The difference between the 2 variables is the distance between vertices: 15.09, according to the metric concept hyperbola.
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