Khan Academy on a Stick : Conic sections

Khan Academy on a Stick

Trigonometry and precalculus

Introduction to Conic Sections
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What are conic sections and why are they called "conic sections"?

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.

Conic Sections: Intro to Circles
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Introduction to the Circle

Circles

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.

Conic Sections: Intro to Ellipses
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Introduction to the ellipse.
Foci of an Ellipse
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Calculating the foci (or focuses) of an Ellipse.

Ellipses

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.

Parabola Focus and Directrix 1
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Parabola as the locus of all points equidistant from a point and a line
Focus and Directrix of a Parabola 2
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Finding the focus and directrix of a parabola

Parabolas

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!

Conic Sections: Intro to Hyperbolas
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Introduction to the hyperbola
Conic Sections: Hyperbolas 2
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Continuation of the intro to hyperbolas
Conic Sections: Hyperbolas 3
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Part 3 of the intro to hyperbolas
Foci of a Hyperbola
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Introduction to the foci (focuses) of a hyperbola
Proof: Hyperbola Foci
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Proof of the hyperbola foci formula

Hyperbolas

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.

Identifying an ellipse from equation
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Part 1 of identifying and graphic conic sections
Identifying a hyperbola from an equation
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Part 2 of identifying and graphing conic sections
Identifying circles and parabolas from equations
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Let's identify (and graph) a couple of more conics!
Hyperbola and parabola examples
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Parabola, Hyperbolas, etc.

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.

Tangent Line Hyperbola Relationship (very optional)
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How a tangent line relates to a hyperbola. Might be useful for some competitive exams where there isn't time to derive (like we are doing in this video)
IIT JEE Circle Hyperbola Common Tangent Part 1
2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tan
IIT JEE Circle Hyperbola Common Tangent Part 2
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2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 2
IIT JEE Circle Hyperbola Common Tangent Part 3
2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 3
IIT JEE Circle Hyperbola Common Tangent Part 4
2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 4
IIT JEE Circle Hyperbola Common Tangent Part 5
2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 5
IIT JEE Circle Hyperbola Intersection
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2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection

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.