Find the length of the major or minor axes of an ellipse

Learning Objectives Identify the standard form of an ellipse equation, whether centered at the origin or at (h, k). Determine if an ellipse has a horizontal or vertical orientation based on its equation. Accurately extract the values of a² and b² from the standard equation of an ellipse. Calculate the values of 'a' (the semi-major axis) and 'b' (the semi-minor axis). Apply the formula 2a to find the length of the major axis. Apply the formula 2b to find the length of the minor axis. Solve problems where the ellipse equation must first be converted into standard form. Ever wondered about the shape of a planet's orbit or the design of a 'whispering gallery'? They're ellipses! Let's explore their key dimensions. 🪐 This tutorial w...

TermDefinitionExample EllipseA set of all points in a plane where the sum of the distances from two fixed points, called the foci, is constant. Visually, it looks like a stretched or flattened circle.The equation \(\frac{x^2}{9} + \frac{y^2}{4} = 1\) describes an ellipse centered at the origin. Major AxisThe longest diameter of an ellipse. It passes through the center and the two vertices. Its length is always 2a.For an ellipse that is wider than it is tall, the major axis is the horizontal line segment connecting its leftmost and rightmost points. Minor AxisThe shortest diameter of an ellipse. It passes through the center and the two co-vertices, and is perpendicular to the major axis. Its length is always 2b.For an ellipse that is wider than it is tall, the minor axis is the vertical li...

Standard Equation of a Horizontal Ellipse \(\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\), where \(a > b > 0\) Use this form when the ellipse is wider than it is tall. The larger denominator, a², is under the x-term. The center is at (h, k). Standard Equation of a Vertical Ellipse \(\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1\), where \(a > b > 0\) Use this form when the ellipse is taller than it is wide. The larger denominator, a², is under the y-term. The center is at (h, k). Formulas for Axis Lengths Length of Major Axis = \(2a\) and Length of Minor Axis = \(2b\) After identifying 'a' (from \(\sqrt{larger \, denominator}\)) and 'b' (from \(\sqrt{smaller \, denominator}\)), use these formulas to find the full lengths of the axes....