Analytic geometry | Algebraic curves | Conic sections
In mathematics, a hyperbola (/haɪˈpɜːrbələ/; pl. hyperbolas or hyperbolae /-liː/; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Hyperbolas arise in many ways: * as the curve representing the reciprocal function in the Cartesian plane, * as the path followed by the shadow of the tip of a sundial, * as the shape of an open orbit (as distinct from a closed elliptical orbit), such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or, more generally, any spacecraft (or celestial object) exceeding the escape velocity of the nearest planet or other gravitational body, * as the scattering trajectory of a subatomic particle (acted on by repulsive instead of attractive forces but the principle is the same), * in radio navigation, when the difference between distances to two points, but not the distances themselves, can be determined, and so on. Each branch of the hyperbola has two arms which become straighter (lower curvature) further out from the center of the hyperbola. Diagonally opposite arms, one from each branch, tend in the limit to a common line, called the asymptote of those two arms. So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve the asymptotes are the two coordinate axes. Hyperbolas share many of the ellipses' analytical properties such as eccentricity, focus, and directrix. Typically the correspondence can be made with nothing more than a change of sign in some term. Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and quantum mechanics which is not Euclidean). (Wikipedia).
Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning
Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an
From playlist Maths Topics
What is the definition of a hyperbola
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
Algebra Ch 40: Hyperbolas (1 of 10) What is a Hyperbola?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn a hyperbola is a graph that result from meeting the following conditions: 1) |d1-d2|=constant (same number) 2) the grap
From playlist THE "HOW TO" PLAYLIST
What is the definition of a hyperbola
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal)
This video provides an example of how to graph and find the major components of a hyperbola given the standard equation of the hyperbola. The hyperbola has a horizontal transverse axis. Site: http:/mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Graphing and Writing Equations of Hyperbolas
Comparing hyperbolas to ellipse's
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
what is the formula's for the asymptotes of a hyperbola
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
MATH1050 Lec 30 Hyperbolas College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
This conic sections video tutorial provides a basic introduction into hyperbolas. It explains how to graph hyperbolas and how to find the coordinates of the center, vertices, and foci. In addition, it explains how to write the equations of the asymptotes. Get The Full 1 Hour 40 Minute V
From playlist New Calculus Video Playlist
Conic Sections: The Hyperbola part 1 of 2
This video defines a hyperbola and explains how to graph a hyperbola given in standard form. http://mathispower4u.wordpress.com/
From playlist Introduction to Conic Sections
Foci of a hyperbola | Conic sections | Algebra II | Khan Academy
Introduction to the foci (focuses) of a hyperbola Watch the next lesson: https://www.khanacademy.org/math/algebra2/conics_precalc/hyperbolas-precalc/v/proof-hyperbola-foci?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/a
From playlist Precalculus | High School Math | Khan Academy
what is the characteristics and formula for a horizontal hyperbola
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
Graphing Hyperbolas in Standard Form
I introduce the basic structure of hyperbolas discussing how to locate the vertices, foci, transverse axis, conjugate axis, asymptotes, etc. I finish by working through multiple examples. Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and t
From playlist PreCalculus
IIT JEE circle hyperbola common tangent part 1 | Conic sections | Algebra II | Khan Academy
2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tan Watch the next lesson: https://www.khanacademy.org/math/algebra2/conics_precalc/jee_hyperbolas/v/iit-jee-circle-hyperbola-common-tangent-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? ht
From playlist Precalculus | High School Math | Khan Academy
Hyperbola (Part 1) | Conic Sections | Don't Memorise
Hyperbola is a special type of curve which looks like two parabolas which are mirror images of each other. But it is actually completely different in nature than a parabola. Watch this video to know what exactly is the hyperbola definition (Hyperbola) and how useful it is. To watch more
From playlist High School Math
In this video, we look at hyperbolas: How to graph them, how to find the asymptotes of hyperbolas, how to find the x and y intercepts of hyperbolas. Hyperbolas are the reciprocal of linear functions, and this provides an easy way to remember which side the hyperbola is on. 👍 If you like
From playlist Functions