This fixed distance difference is twice that of A, where A is the distance from the center of hyperbola to the vertex of the nearest branch of hyperbola. A is also called the real semi-axis of hyperbola. The focal point is located on the through axis, and the middle point is called the center, which is generally located at the origin.
Mathematically, hyperbola (multiple hyperbola or hyperbola) is a smooth curve on a plane, which is defined by the equation of its geometric characteristics or the combination of its solutions. A hyperbola has two parts, called connected components or branches, which are mirror images of each other, similar to two infinite bows.
Hyperbola is one of the three conic curves formed by the intersection of plane and double cone. Other conical parts are parabolas and ellipses, and circles are special cases of ellipses. If the plane intersects the two halves of a double cone, but does not pass through the vertex of the cone, the conic curve is a hyperbola.
Application of hyperbola in real life;
According to geometry, the locus of a point with a constant distance difference from two fixed points on a sphere is a spherical hyperbola focusing on these two fixed points. Hyperbolic navigation system is established and named according to this geometric principle.
If a radio signal transmitting station is set at each of the two focus positions and a radio pulse signal is transmitted at the same time; The ship's radio receiver receives these pulse signals, and determines the distance difference between the ship and the two transmitting stations according to the time difference or phase difference of the received signals, so that the ship's position at this time can be determined to be on the hyperbola corresponding to the measured distance difference.
If two pairs of radio transmitting stations are set, two sets of intersecting hyperbolic families can be obtained. The receiver on the ship receives two pairs of radio signals to obtain two hyperbolic ship lines; The intersection of two ship lines is the position of the ship when measuring.