Conic Sections: The Ellipse

In this lesson, we will continue learning about conic sections, with a specific focus on the ellipse. We will begin by learning about the standard forms of an ellipse when centered at the origin. This comes from the definition of an ellipse where it is the set of all points in a plane, the sum of whose distances from two fixed points, known as the foci, is constant. From there, we will learn about the major axis and its endpoints, the vertices, along with the minor axis and its endpoints, the covertices. We will learn how to find the equation of an ellipse in standard form given certain information such as the foci and vertices. Additionally, we will learn how to write the standard form of the equation of an ellipse given the general form. Lastly, we will see how to shift the graph when the center is given as some (h, k), which is not the origin.