Introduction to conic sections  Conic sections  Algebra II  Khan Academy  Summary and Q&A
TL;DR
Conic sections refer to the intersection of a plane and a cone, resulting in shapes like circles, ellipses, parabolas, and hyperbolas.
Questions & Answers
Q: How are conic sections named?
Conic sections are named because they are formed by the intersection of a plane and a cone, resulting in shapes like circles, ellipses, parabolas, and hyperbolas.
Q: What is the relationship between circles and ellipses?
Circles are a special case of ellipses, where they are perfectly symmetrical and not stretched more in one dimension than the other.
Q: How can parabolas be represented by equations?
Parabolas can be represented by equations such as y = x^2 or x = y^2, and they can be shifted or rotated.
Q: What are the characteristics of hyperbolas?
Hyperbolas have two curves that resemble open Ushapes and can be oriented in various directions. They approach asymptotes as they get closer to them.
Summary & Key Takeaways

Conic sections are shapes formed by the intersecting of a plane and a cone, and they include circles, ellipses, parabolas, and hyperbolas.

Circles are equidistant points from a center, while ellipses are squished circles and can be tilted.

Parabolas have a Ushape and can be represented by equations like y = x^2 or x = y^2.

Hyperbolas have two curves that resemble open Ushapes and can be represented in various orientations.