# Conic sections

Contents
Learn about the four conic sections and their equations: Circle, Ellipse, Parabola, and Hyperbola.

## 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.