Analytic Geometry: Conic Sections

Video Lectures

Displaying all 39 video lectures.
Lecture 1
Parabolas, Part 1
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Parabolas, Part 1
Conic Sections: Parabolas, Part 1. In this video, I discuss a quick way to roughly sketch a parabola. Nothing about directrix and focus in this video (look in part 2!). I simply find the vertex, x and y intercepts and do a quick graph.
Lecture 2
Parabolas, Part 2 (Directrix and Focus)
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Parabolas, Part 2 (Directrix and Focus)
Conic Sections: Parabolas, Part 2 (Directrix and Focus). In this video, I discuss how to go about finding the directrix and the focus for a parabola and do a couple of examples.
Lecture 3
Parabolas, Part 3 (Focus and Directrix)
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Parabolas, Part 3 (Focus and Directrix)
Conic Sections: Parabolas, Part 3 ( Focus and Directrix). Just another example of finding the focus and directrix for a parabola (a slightly more involved example).
Lecture 4
Parabolas, Part 4 (Focus and Directrix)
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Parabolas, Part 4 (Focus and Directrix)
Conic Sections: Parabolas, Part 4 (Focus and Directrix). In this video, I find the equation for a parabola given the vertex and given the focus and/or directrix.
Lecture 5
Parabola: Find the Focus and Directrix
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Parabola: Find the Focus and Directrix
Conic Sections, Parabola : Find the Focus and Directrix. In this video, we find the focus and directrix of a parabola.
Lecture 6
Parabola: Sketch Graph by Finding Focus, Directrix, Points
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Parabola: Sketch Graph by Finding Focus, Directrix, Points
Conic Sections, Parabola: Sketch Graph by Finding Focus, Directrix, Points. In this video, I sketch the graph of a parabola by first finding the directrix and focus followed by plotting a few points.
Lecture 7
Parabola: Find Equation of Parabola Given the Focus
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Parabola: Find Equation of Parabola Given the Focus
Conic Sections, Parabola : Find Equation of Parabola Given the Focus. In this example, we are given that a parabola has a vertex at the origin and we are given the coordinates of the focus. From that, we find the equation of the parabola.
Lecture 8
Parabola: Find Equation of Parabola Given Directrix
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Parabola: Find Equation of Parabola Given Directrix
Conic Sections, Parabola : Find Equation of Parabola Given Directrix. In this example, we are given that a parabola has a vertex at the origin and we are given the equation of the directrix. From that, we find the equation of the parabola.
Lecture 9
Parabola, Shifted: Find Equation Given Vertex and Focus
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Parabola, Shifted: Find Equation Given Vertex and Focus
Conic Sections, Parabola, Shifted : Find Equation Given Vertex and Focus. Here we find the equation of a shifted parabola given information about the vertex and the focus.
Lecture 10
Hyperbolas, An Introduction - Graphing Example
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Hyperbolas, An Introduction - Graphing Example
Conic Sections: Hyperbolas, An Introduction - Graphing Example. In this video, I graph a hyperbola by finding the center, foci, vertices, and asymptotes.
Lecture 11
Finding the Equation for a Hyperbola Given the Graph - Example 1
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Finding the Equation for a Hyperbola Given the Graph - Example 1
Finding the Equation for a Hyperbola Given the Graph - Example 1.
Lecture 12
Finding the Equation for a Hyperbola Given the Graph - Example 2
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Finding the Equation for a Hyperbola Given the Graph - Example 2
Finding the Equation for a Hyperbola Given the Graph - Example 2. In this example, we are given the foci and vertices and use those to find the equation of the hyperbola. (I still make a sketch at the beginning though!)
Lecture 13
Hyperbola: Graphing a Hyperbola
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Hyperbola: Graphing a Hyperbola
Conic Sections, Hyperbola : Graphing a Hyperbola.
In this example, we are given the equation of a hyperbola; I show how to do a rough graph.
Lecture 14
Hyperbola: Find Equation Given Foci and Vertices
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Hyperbola: Find Equation Given Foci and Vertices
Conic Sections, Hyperbola: Find, Equation Given Foci and Vertices. In this example, we are given the vertices and the foci of an ellipse. We then find the equation of the ellipse.
Lecture 15
Hyperbola: Find Equation Gvien Focus, Transverse Axis Length
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Hyperbola: Find Equation Gvien Focus, Transverse Axis Length
Conic Sections, Hyperbola: Find Equation Gvien Focus, Transverse Axis Length
Lecture 16
Hyperbola: Find Equation Given Vertices and Asymptotes
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Hyperbola: Find Equation Given Vertices and Asymptotes
Conic Sections, Hyperbola : Find Equation Given Vertices and Asymptotes.
Here we find the equation of a conic section given information about the vertices and the asymptotes.
Lecture 17
Hyperbola: Word Problem , Finding an Equation
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Hyperbola: Word Problem , Finding an Equation
Conic Sections, Hyperbola : Word Problem , Finding an Equation.
In this example we have to find the equation that represents the hyperbolic path on which a ship is traveling.
Lecture 18
Hyperbola, Shifted: Find Asymptotes
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Hyperbola, Shifted: Find Asymptotes
Conic Sections, Hyperbola , Shifted : Find Asymptotes. Here we find the point-slope form of the asymptotes of a hyperbola.
Lecture 19
Conic Sections, Hyperbola, Shifted: Sketch the Graph
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Conic Sections, Hyperbola, Shifted: Sketch the Graph
Conic Sections, Hyperbola, Shifted: Sketch the Graph. Here we sketch the graph of a shifted hyperbola.
Lecture 20
Conic Sections: Graphing Ellipses (Part 1)
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Conic Sections: Graphing Ellipses (Part 1)
Conic Sections: Graphing Ellipses Part 1.
In this video, I give the basic definition, one standard formula, and graph two ellipses given the equation.
In part 2, I graph two harder examples.
Lecture 21
Conic Sections: Graphing Ellipses (Part 2)
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Conic Sections: Graphing Ellipses (Part 2)
Conic Sections: Graphing Ellipses Part 2. In this video, I graph two more ellipses. The second examples requires completing the square to put it in a 'standard form'.
Lecture 22
Ellipse: Graph the Ellipse
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Ellipse: Graph the Ellipse
Conic Sections, Ellipse : Graph the Ellipse.
In this video, I show an example of graphing an ellipse!
Lecture 23
Find Equation of an Ellipse Given Major / Minor Axis Length
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Find Equation of an Ellipse Given Major / Minor Axis Length
Conic Sections: Find Equation of an Ellipse Given Major / Minor Axis Length. In this video, we have an ellipse centered at the origin with a specified major and minor axis length. I show how to find the equation of the ellipse with this information.
Lecture 24
Ellipse: Find the Equation Given the Foci and Intercepts
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Ellipse: Find the Equation Given the Foci and Intercepts
Conic Sections, Ellipse : Find the Equation Given the Foci and Intercepts.
In this example, we are given an ellipse is centered at the origin, the foci of the ellipse and intercepts along the minor axis. We then find the equation of the ellipse using this information.
Lecture 25
Ellipse: Find Equation given Foci and Minor Axis Length
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Ellipse: Find Equation given Foci and Minor Axis Length
Conic Sections, Ellipse : Find Equation given Foci and Minor Axis Length.
Lecture 26
Ellipse: Find X and Y Intercepts
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Ellipse: Find X and Y Intercepts
Conic Sections, Ellipse : Find X and Y Intercepts. In this video, we find the x and y intercepts of an ellipse centered at the origin.
Lecture 27
Ellipse: Find the Foci of an Ellipse
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Ellipse: Find the Foci of an Ellipse
Conic Sections , Ellipse : Find the Foci of an Ellipse.
Here we are given the equation of an ellipse and proceed to find the foci.
Lecture 28
Ellipse: Find the Foci Given Eccentricity and Vertices
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Ellipse: Find the Foci Given Eccentricity and Vertices
Conic Sections, Ellipse : Find the Foci Given Eccentricity and Vertices. Just like it says! We are given the eccentricity and the vertices of an ellipse and proceed to find the foci.
Lecture 29
Ellipse: Find Equation Given Eccentricity and Vertices
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Ellipse: Find Equation Given Eccentricity and Vertices
Conic Sections, Ellipse : Find Equation Given Eccentricity and Vertices. In this video, we find the equation of an ellipse that is centered at the origin given information about the eccentricity and the vertices.
Lecture 30
Hyperbola: Find Equation Given Foci and Vertices
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Hyperbola: Find Equation Given Foci and Vertices
Conic Sections, Hyperbola: Find, Equation Given Foci and Vertices. In this example, we are given the vertices and the foci of an ellipse. We then find the equation of the ellipse.
Lecture 31
Conic Sections, Ellipse, Shifted: Sketch Graph Given Equation
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Conic Sections, Ellipse, Shifted: Sketch Graph Given Equation
Conic Sections, Ellipse, Shifted: Sketch Graph Given Equation. In this example, we sketch the graph of a shifted ellipse.
Lecture 32
The Center-Radius Form for a Circle - A few Basic Questions, Example 1
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The Center-Radius Form for a Circle - A few Basic Questions, Example 1
The Center-Radius Form for a Circle - A few Basic Questions, Example 1
Lecture 33
The Center-Radius Form for a Circle - A few Basic Questions, Example 2
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The Center-Radius Form for a Circle - A few Basic Questions, Example 2
The Center-Radius Form for a Circle - A few Basic Questions, Example 2
Lecture 34
Finding the Center-Radius Form of a Circle by Completing the Square - Example 1
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Finding the Center-Radius Form of a Circle by Completing the Square - Example 1
Finding the Center-Radius Form of a Circle by Completing the Square - Example 1
Lecture 35
Finding the Center-Radius Form of a Circle by Completing the Square - Example 2
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Finding the Center-Radius Form of a Circle by Completing the Square - Example 2
Finding the Center-Radius Form of a Circle by Completing the Square - Example 2
Lecture 36
Finding the Center-Radius Form of a Circle by Completing the Square - Example 3
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Finding the Center-Radius Form of a Circle by Completing the Square - Example 3
Finding the Center-Radius Form of a Circle by Completing the Square - Example 3
Lecture 37
Identifying a Conic from an Equation by Completing the Square, Ex 1
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Identifying a Conic from an Equation by Completing the Square, Ex 1
Identifying a Conic from an Equation by Completing the Square, Ex 1. In this video, I take an equation and complete the square so that we can better recognize the type of conic given by the equation.
For more free math videos, visit: http://PatrickJMT.com
Lecture 38
Identifying a Conic from an Equation by Completing the Square, Ex 2
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Identifying a Conic from an Equation by Completing the Square, Ex 2
Identifying a Conic from an Equation by Completing the Square, Ex 2. In this video, I take an equation and complete the square so that we can better recognize the type of conic given by the equation.
For more free math videos, visit: http://PatrickJMT.com
Lecture 39
Identifying a Conic from an Equation by Completing the Square, Ex 3
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Identifying a Conic from an Equation by Completing the Square, Ex 3
Identifying a Conic from an Equation by Completing the Square, Ex 3. In this video, I take an equation and complete the square so that we can better recognize the type of conic given by the equation.
For more free math videos, visit: http://PatrickJMT.com