Conic sections

This course is a part of Algebra (all content), a 20-course Topic series from Khan Academy.

This topic covers the four conic sections and their equations: Circle, Ellipse, Parabola, and Hyperbola.

This course contains 12 segments:

Introduction to conic sections

Conic sections are formed when you intersect a plane with a cone. In this tutorial, you will learn more about what makes conic sections special.

The features of a circle

Learn about the graphs of circles, and how their center and radius are represented algebraically.

Standard equation of a circle

Learn about the standard form to represent a circle with an equation. For example, the equation (x-1)^2+(y+2)^2=9 is a circle whose center is (1,-2) and radius is 3.

Expanded equation of a circle

Learn how to analyze an equation of a circle that is not given in the standard form. For example, find the center of the circle whose equation is x^2+y^2+4x-5=0.

Center and radii of an ellipse

Learn about the basic features of ellipses: their center and the two radii that pass through it, the major radius and the minor radius.

Foci of an ellipse

Learn about the foci of an ellipse, which are two points for which the sum of the distances from any point on the ellipse is constant.

Focus and directrix of a parabola

A parabola is the set of all points equidistant from a point (called the focus) and a line (called the directrix). In this tutorial you will learn about the focus and the directrix, and how to find the equation of a parabola given its focus and directrix.

Introduction to hyperbolas

A hyperbola is the set of all points whose distances from two specific points (called the foci) have the same difference. Learn more about it here.

Foci of a hyperbola

Learn about the foci of the hyperbola: How to find them from the hyperbola's equation and how to find the equation when given the foci.

Hyperbolas not centered at the origin

Generalize what you learned about hyperbolas to study hyperbolas whose center can be any point.

Identifying conic sections from their expanded equations

Learn how to analyze expanded equations in order to determine which kind of conic section they represent.

Challenging conic section problems (IIT JEE)

See Sal solve two (very) advanced problems from the IIT JEE exam, a highly challenging exam administered in India.