Learning Outcomes: Determine the equation of the ellipse with centre and foci or . (a) Vertices of an ellipse are defined as the end points of the major axis (b) Show all the vertices, foci, major and minor axes. Sketch ellipses, recognize the shape and label the centre, vertices & foci. Determine the centre and foci of an ellipse by using completing the square method. (c) At the end of the lesson, students should be able to 4.2 Ellipses C04 - SM025 Page 1
Centre: Foci: Vertices: Length of Standard Equation: [wtih ] General Equation: Graph reference: https://www.desmos.com/calculator/fbidvhghvt Centre at origin Centre: Foci: Vertices: Length of Standard Equation: [wtih ] General Equation: The Equation of an Ellipses (horizontal major axis) C04 - SM025 Page 2
Given an ellipse with the equation . Determine the centre, foci, vertices, the length of major and minor axes. Solution: Centre: Foci: Vertices: Length of Remarks: Major axis : Minor axis : Graph: Example 1* C04 - SM025 Page 3
Standard Equation: [wtih ] Centre: Foci: Vertices: Length of General Equation: Graph reference: https://www.desmos.com/calculator/qbbxwq2eyi Centre at origin Centre: Foci: Vertices: Length of Standard Equation: [wtih ] General Equation: The Equation of an Ellipse (vertical major axis) C04 - SM025 Page 4
Given an ellipse with the equation . Determine the centre, foci, vertices, the length of major and minor axes. Solution: Centre: Foci: Vertices: Length of Remarks: Major axis : Minor axis : Graph: Example 2* C04 - SM025 Page 5
Find the equation of an ellipse with centre at , one focus at and one vertex at Hence, graph the equation. Solution : Ellipse equation: Graph: Example 3 C04 - SM025 Page 6
. Given the equation (a) Show that the equation given represent an ellipse. Solution : [Standard Equation of an Ellipse] [Shown] (b) Hence, determine the centre and the foci of the ellipse. Solution : Centre: Foci: Example 4 C04 - SM025 Page 7
An ellipse has foci at the points and . If the length of the major axis of this ellipse is 10 units, determine its equation. Hence, sketch its graph. Solution : [midpoint of the foci] Ellipse equation: Graph: Centre: Foci: Vertices: Example 5 C04 - SM025 Page 8