Graphing Ellipses and Finding Foci and Vertices

The Organic Chemistry Tutor

This comprehensive math tutorial provides a detailed guide on understanding, graphing, and writing equations for ellipses, a key topic in Algebra II and Pre-Calculus. The video breaks down the anatomy of an ellipse, distinguishing between horizontal and vertical major axes and explaining the significance of the variables a, b, and c. It introduces the standard equations for ellipses centered at the origin as well as those shifted to a center point (h, k), clarifying how to determine the orientation of the shape based on the denominators in the equation. The content explores the mathematical relationships governing ellipses, specifically the formula c² = a² - b² used to locate the foci. Through a series of step-by-step examples, viewers learn how to identify the center, calculate the lengths of the major and minor axes, and determine the precise coordinates of the vertices and foci. The video progresses from basic examples centered at the origin to more complex problems involving translations, ensuring students understand how standard transformations apply to conic sections. This resource is highly valuable for the classroom as it bridges the gap between algebraic formulas and geometric graphs. It offers clear, procedural knowledge for solving ellipse problems, making it an excellent tool for introducing the topic, remediation, or test review. Teachers can use the specific practice problems to model problem-solving strategies, while the visual approach helps students conceptually grasp how changing specific parameters in the equation directly affects the shape and position of the graph.