Watch Conic Sections

Conic Sections is a math show hosted by Brian McLogan on Free Math Videos. This series explores the different types of conic sections, their properties, and how to graph them. Conic sections are the resulting shapes formed when a plane intersects a double-napped cone in varying angles and distances. These shapes include circles, ellipses, parabolas, and hyperbolas.

The series starts with an introduction to conic sections and how to identify them based on their characteristic equations. Brian explains the general form of a second-degree equation and how it relates to each of the four types of conic sections. He also reveals some real-world applications of conic sections in fields such as astronomy, architecture, and physics.

Next, Brian dives into circles – the simplest conic section. He covers the definition of a circle, its equation, and how to graph it. He then explores the different properties of circles such as their radius, area, circumference, and diameter. Additionally, he explains how to find the equation of a circle given its center and radius or given three points.

The series then progresses to ellipses, the second type of conic section. Brian explains the definition of an ellipse, its standard equation, and how to graph it. He also covers the main features of an ellipse such as its foci, vertices, axis lengths, and eccentricity. Brian further provides techniques for locating the foci and center of an ellipse given its equation, and for finding the equation of an ellipse given its major and minor axes.

After ellipses, the series moves on to parabolas – the third type of conic section. Brian expounds on the definition of a parabola, its standard equation, and how to graph it. He discusses the various shapes of parabolas depending on the coefficient of its quadratic term. Moreover, he shows how to find the vertex, axis of symmetry, focus, and directrix of a parabola given its equation.

Lastly, the series concludes with hyperbolas – the fourth type of conic section. Brian unpacks the definition of a hyperbola, its standard equation, and how to graph it. He then covers the essential features of a hyperbola such as its foci, vertices, center, asymptotes, and transverse and conjugate axes. He also shows how to find the equation of a hyperbola given its foci and asymptotes or given its vertices and one point on its curve.

Throughout the series, Brian employs a clear and concise teaching style that makes even complex concepts easy to understand. He uses visuals such as diagrams, graphs, and real-life examples to illustrate each topic. He also provides practice problems at the end of each video to help viewers solidify their understanding.

Overall, Conic Sections is an excellent resource for anyone looking to learn or review the fundamentals of conic sections. Whether you are a student preparing for a test, a teacher in need of curriculum support, or a lifelong learner interested in math concepts, this series delivers thorough explanations and practical applications of conic sections.