Euclidean solid geometry | Birational geometry | Conic sections | Algebraic curves | Analytic geometry
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a focus, and some particular line, called a directrix, are in a fixed ratio, called the eccentricity. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is, as the set of points whose coordinates satisfy a quadratic equation in two variables which can be written in the form The geometric properties of the conic can be deduced from its equation. In the Euclidean plane, the three types of conic sections appear quite different, but share many properties. By extending the Euclidean plane to include a line at infinity, obtaining a projective plane, the apparent difference vanishes: the branches of a hyperbola meet in two points at infinity, making it a single closed curve; and the two ends of a parabola meet to make it a closed curve tangent to the line at infinity. Further extension, by expanding the real coordinates to admit complex coordinates, provides the means to see this unification algebraically. (Wikipedia).
Learn how to classify conic sections
Learn how to classify conic sections. A conic section is a figure formed by the intersection of a plane and a cone. A conic section may be a circle, an ellipse, a parabola, or a hyperbola. The general equation of a conic section is given by Ax^2 + By^2 + Cx + Dy + E = 0. When given the ge
From playlist The Hyperbola in Conic Sections
Learn how to classify conic sections
Learn how to classify conic sections. A conic section is a figure formed by the intersection of a plane and a cone. A conic section may be a circle, an ellipse, a parabola, or a hyperbola. The general equation of a conic section is given by Ax^2 + By^2 + Cx + Dy + E = 0. When given the ge
From playlist The Hyperbola in Conic Sections
Steps to classify conic sections
Learn how to classify conic sections. A conic section is a figure formed by the intersection of a plane and a cone. A conic section may be a circle, an ellipse, a parabola, or a hyperbola. The general equation of a conic section is given by Ax^2 + By^2 + Cx + Dy + E = 0. When given the ge
From playlist The Hyperbola in Conic Sections
Determining What Type of Conic Section from General Form
This video explains how to determine if a given equation in general form is a circle, ellipse, parabola, or hyperbola. http://mathispower4u.wordpress.com/
From playlist Introduction to Conic Sections
Conics What are the important parts of a horizontal ellipse
Learn all about ellipses for conic sections. We will discuss all the essential definitions such as center, foci, vertices, co-vertices, major axis and minor axis. We will also discuss the essential processes such as how to graph and writing the equation based on if it has a horizontal or
From playlist The Ellipse in Conic Sections
Conic Sections: The Parabola part 1 of 2
This video defines a parabola and explains how to graph a parabola in standard form. http://mathispower4u.wordpress.com/
From playlist Introduction to Conic Sections
A conic section is the intersection of a plane and a cone. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines. parabola, 2 parallel line
From playlist Maths Topics
Introduction to Conic Sections
This video shows how you can generate a circle, ellipse, parabola, and hyperbola by intersecting a cone with a plan. It is the first of several videos on the conic sections. http://mathispower4u.wordpress.com/
From playlist Introduction to Conic Sections
What is the definition of a parabola for CONIC sections
Learn all about parabolas in conic sections. We will discover the basic definitions such as the vertex, focus, directrix, and axis of symmetry. We will also take a look a basic processes such as graphing, writing the equation and identifying a parabolas parts when given an equation in sta
From playlist Learn all about Parabolas #Conics
How to Draw Tangent Circles using Cones
Solving the Problem of Apollonius with Conic Sections This video describes a non-standard way of finding tangent circles to a given set of 3 circles, known as the Problem of Apollonius. It uses conic sections rather than straightedge and compass. I feel this approach is more intuitive and
From playlist Summer of Math Exposition Youtube Videos
Introduction to conic sections | Conic sections | Algebra II | Khan Academy
What are conic sections and why are they called "conic sections"? Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/conics_precalc/conic_section_intro/e/recognizing_conic_sections?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Wa
From playlist Precalculus | High School Math | Khan Academy
Making a Mirror with a Variable Surface Shape
Some concepts in this video have been pictured in a somewhat simplified manner to make it more accessible to a less specialized audience. Contents: 00:00 General intro 00:56 Conic constant explained 10:00 Explanation of the manufacturing process 12:25 Testing the mirror 15:32 interferom
From playlist optics
Before learning conic sections know this....
In this video we are going to explore what you need to know before learning conics. 👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1 ❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join 🗂️
From playlist Conics - Brian McLogan
Conic Loaf of Bread - Numberphile
Featuring Cliff Stoll - http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ Cliff's website: https://www.kleinbottle.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Scienc
From playlist Cakes & Cutting on Numberphile
Master Determing the vertex, focus and directrix of a parabola by completing the square
Subscribe! http://www.freemathvideos.com Want more math video lessons? Visit my website to view all of my math videos organized by course, chapter and section. The purpose of posting my free video tutorials is to not only help students but allow teachers the resources to flip their classro
From playlist Conic Sections #Master
Eccentricity and directrix of the conic section (KristaKingMath)
â–ş My Polar & Parametric course: https://www.kristakingmath.com/polar-and-parametric-course Learn how to use the polar equation of a conic section to identify the conic as a parabola, an ellipse, or a hyperbola, find eccentricity and the equation of the directrix, and the sketch the conic.
From playlist Polar & Parametric