Khan Academy on a Stick

Conic section basics

What is a conic other than a jazz singer from New Orleans? Well, as you'll see in this tutorial, a conic section is formed when you intersect a plane with cones. You end up with some familiar shapes (like circles and ellipses) and some that are a bit unexpected (like hyperbolas). This tutorial gets you set up with the basics and is a good foundation for going deeper into the world of conic sections.


You've seen circles your entire life. You've even studied them a bit in math class. Now we go further, taking a deep look at the equations of circles.


What would you call a circle that isn't a circle? One that is is is taller or fatter rather than being perfectly round? An ellipse. (All circles are special cases of ellipses.) In this tutorial we go deep into the equations and graphs of ellipses.


You've seen parabolas already when you graphed quadratic functions. Now we will look at them from a conic perspective. In particular we will look at them as the set of all points equidistant from a point (focus) and a line (directrix). Have fun!


It is no hyperbole to say that hyperbolas are awesome. In this tutorial, we look closely at this wacky conic section. We pay special attention to its graph and equation.

Conics from equations

You're familiar with the graphs and equations of all of the conic sections. Now you want practice identifying them given only their equations. You, my friend, are about to click on exactly the right tutorial.

Conics in the IIT JEE

Do you think that the math exams that you have to take are hard? Well, if you have the stomach, try the problem(s) in this tutorial. They are not only conceptually difficult, but they are also hairy. Don't worry if you have trouble with this. Most of us would. The IIT JEE is an exam administered to 200,000 students every year in India to select which 2000 go to the competitive IITs. They need to make sure that most of the students can't do most of the problems so that they can really whittle the applicants down.