Find the center, vertices, or co-vertices of an ellipse

Learning Objectives Identify the center (h, k) of an ellipse from its standard equation. Determine whether an ellipse has a horizontal or vertical major axis by comparing denominators. Calculate the values of 'a' (major radius) and 'b' (minor radius) from the equation. Find the exact coordinates of the vertices. By the end of a this lesson, students will be able to find the exact coordinates of the co-vertices. Distinguish between vertices and co-vertices and relate them to the major and minor axes. Ever wondered about the shape of a planet's orbit or the design of a 'whispering gallery' where a secret can be heard across the room? 🪐 They're all based on the ellipse! In this tutorial, we will break down the standard equation of an el...

TermDefinitionExample EllipseA flattened circle; the set of all points in a plane where the sum of the distances from two fixed points (the foci) is constant.The path the Earth takes around the Sun is an ellipse. Center (h, k)The midpoint of both the major and minor axes. It is the central point from which the ellipse is symmetric.In the ellipse equation (x-3)^2/16 + (y+2)^2/9 = 1, the center is at the point (3, -2). Major AxisThe longer axis of an ellipse, passing through the center and the two vertices. Its length is 2a.If an ellipse is wider than it is tall, its major axis is horizontal. VerticesThe endpoints of the major axis. They are the two points on the ellipse that are farthest from the center.For a horizontal ellipse centered at (0,0) with a=5, the vertices are at (5,0) and (-5,...

Standard Equation of a Horizontal Ellipse \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 Use this form when the ellipse is wider than it is tall. The larger denominator, a^2, is under the x-term. Here, a > b. The center is (h, k), vertices are (h±a, k), and co-vertices are (h, k±b). Standard Equation of a Vertical Ellipse \frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1 Use this form when the ellipse is taller than it is wide. The larger denominator, a^2, is under the y-term. Here, a > b. The center is (h, k), vertices are (h, k±a), and co-vertices are (h±b, k).