In mathematics, a hyperbola is a smooth curve that lies on a plane represented by its geometric properties or equations, representing a series of solutions. The hyperbola consists of two parts: connected components or branches; each part is a mirror image. They are like two endless arches. A hyperbola calculator provides one of three conical cross-sections formed by the intersection of a plane and a double cone.
Hyperbola
In a hyperbola, the plane cuts a double cone in half but does not pass through the cone’s apex. The other two cones are elliptical and parabolic. The hyperbola equation calculator uses an equation with the origin as the center is defined as follows:
(x2 / a2)-(y2 / b2) = 1
The asymptote of the line:
y = (b / a) x
y =-(b/a) x
Hyperbola appears in different ways:
- As a curve representing the function y(x) = 1/x on the Cartesian plane,
- As followed, The path of the sun d covered by spikes, shaped like an open orbit (as opposed to a closed elliptical orbit), like the orbit of a spacecraft rotating under the action of gravity, or more, anything beyond the next planet Speed of spacecraft planets.
- For example, the path of a comet with a single appearance (moving too fast to return to the solar system)
- The scattering path of subatomic particles (repulsive force acts on it instead of gravity, but the principle is the same)
- In radio navigation In, is it possible to determine the difference between the distances to two points, but not the distance itself?
As a locus of a point
A hyperbola can be geometrically defined as a set of Euclidean planes Point (a set of points):
A hyperbola calculator provides a group of points so that for each point P in the group, the distance has
| PF1 |, | | PF2 | at two fixed points F1, F2 (focus) is constant, usually expressed by 2a, a> 0:
H = {P: | |PF2 | – PF1| | = 2a
The center M of the line segment connecting the foci point is called the center of the hyperbola. The line passing through the foci point is called the main axis. It contains corner points V1, V2, and the distance between these corner points and the center is a. The distance c from the foci point to the center is called the foci length or linear eccentricity. The quotient c/a is the eccentricity of e.
An equation | |PF2 | – PF1| | = 2a can be viewed differently:
If c2 is a circle with center F2 and radius 2a, then point P on the right branch to circle c2. The distance is equal to the distance to the focal point F2.
| PF1 | = | Pc2 |
C2 is called a hyperbolic circular guide (connected to the foci point of F2). To get the left branch of the hyperbola, you need to use the circular guideline of F2. This property should not be confused with using the guidelines (lines) below to define a hyperbola.
As a flat section of a cone
The hyperbola calculator provides an intersection of a vertical double circular cone, and a plane whose slope is greater than that of the straight line in the cone does not pass through the apex is a hyperbola. To define the properties of the hyperbola, two dandelion balls, d1, d2 are used, which touch the cone at points F1 and F2 along with the circles c1, c2, and the cutting plane (hyperbola). It turns out that F1 and F2 are hyperbolic focal points.
- Let P be any point on the intersecting curve.
- The conical generatrix containing P intersects circle c1 at point A and circle c2 at point B.
- The line segments PF1 and PA contact the sphere d1 and therefore have the same length.
- The feet | PF2 | and |PB| touch the ball d2 and therefore have the same length.
