geometric entity which is called hyperbole - is a flat curve shape of the second order, consisting of two curves which are drawn separately and do not intersect.The mathematical formula to describe it is as follows: y = k / x, if the number under the index k is not equal to zero.In other words, the top of the curve are constantly striving to zero, but never crossed it.From the position of the point of building a hyperbole - is the amount of points on the plane.Each point is characterized by a constant value for the difference of the distance between two focal points.
plane curves distinguish the main features that are inherent only to her:
- Hyperbole - two separate lines called branches.
- In the middle of the axis of a large order is the center of the figure.
- peak called next to each other in terms of the two branches.
- Focal Length is the distance from the center of the curve to one of the foci (denoted by the letter "c").
- major axis of the hyperbole describes the shortest distance between the branches-lines.
- Focuses lie on the major axis, provided the same distance from the center of the curve.Line, which supports the major axis is called a transverse axis.
- Large floor - is the calculated distance from the center of the curve to one of the peaks (indicated by the letter "a").
- straight line perpendicular to the transverse axis passing through its center, called the conjugate axis.
- focal parameter defines the interval between the focus and hyperbole, it is perpendicular to the transverse axis.
- distance between the focus and the asymptote is called the impact parameter and is typically encoded in formulas under the letter «b».
In classical Cartesian-known equation, which can be built on the hyperbole, looks like: (x2 / a2) - (y2 / b2) = 1. The type of curve that has the same axis, called the isosceles.In the Cartesian coordinate system it is possible to describe a simple equation: xy = a2 / 2, with the foci of the hyperbola must be placed at the intersection points (a, a) and (-a, -a).
Each curve can exist parallel to hyperbole.This is her version of the conjugate, in which the axes are reversed, with the asymptote remains in place.Optical properties of the shape is that of an imaginary light source to the one focus is capable of reflecting a second leg and intersecting at the second focus.Any potential point of hyperbole has a constant value of the ratio of the distance to any focus to the distance to the headmistress.A typical flat curve can be both a mirror and rotational symmetry when rotated through 180 ° at the center.
hyperbola Eccentricity determined numerical characteristic of conic section, which shows the degree of deviation from the ideal cross-section of the circle.In mathematical formulas, the figure indicated by the letter "e".Eccentricity is usually invariant with respect to the plane of movement and transformation process of its similarity.Hyperbole - a figure in which the eccentricity is always equal to the ratio between the focal length of the major axis.
