A hyperbola is a plane curve defined by two different points (called focal points), and the ratio of the distances to these two points is constant.
1, the focus is on the x axis.
If the equation of hyperbola is y? /a？ -x？ /b？ = 1, and a? & gtb？ Then the focus of the hyperbola is on the x axis.
2. the focus is on the y axis.
If the equation of hyperbola is x? /a？ -Really? /b？ = 1, and a? & ltb？ Then the focus of the hyperbola is on the y axis.
In these two cases, the shape of hyperbola will be different. When the focus is on the X-axis, both branches of hyperbola have asymptotes on the Y-axis, which is similar to a parallelogram with an upward opening. When the focus is on the Y-axis, the two branches of the hyperbola have asymptotes on the X-axis, which are similar in shape to a parallelogram with an opening to the right.
It is very important to judge whether the focus of hyperbola is on X axis or Y axis, which can help us describe the shape and characteristics of hyperbola more accurately.
Application of hyperbola in coordinates, physical mathematics, economy, engineering and biology;
1, coordinate system
Hyperbola is often used to establish rectangular coordinate system, so that the distance between axes is proportional to a constant.
2. Physics and Mathematics
Hyperbola is an important mathematical model, which is often used to describe problems in physics and mathematics, such as the force between gravitation in physics, wavefront refraction in optics, ellipsoid measurement and orbital motion.
3. Economics and Social Sciences
Hyperbola is used to describe some phenomena in economic and social sciences, such as interest rate, inflation and savings.
4. Engineering and Geometry
Hyperbola is widely used in engineering and geometry, such as constructing orange peel curve route, cone measurement, free-form surface drawing and so on.
5. Biology and Medicine
Hyperboles are also used in biology and medicine. For example, it can be used to describe the changes of human heart rate, respiration and blood sugar. At the same time, hyperbola can also be used to model the spread speed and scope of infectious diseases.