# Conic sections

Contents

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

17 exercises available

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.

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

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.

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.

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

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.

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.

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.

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.

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

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

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