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lesson4.-ellipse f.pptx
- 6. What do you notice about the pictures? IdentifyandDescribethePicture
- 7. LEARNINGOBJECTIVES 01 define an ellipse 03 graph an ellipse in a rectangular coordinate system given an equation with center at (0,0) 02 determine the standard form of equation of an ellipse with center at (0,0)
- 10. Definition of Ellipse An ellipse is a set of points such that the sum of the distances from two fixed points is constant. The fixed points are the foci, and the constant sum is the length of major axis. ELLIPSE F F P(x,y) π1 π2 π1 + π2 = ππππ π‘πππ‘
- 11. The ellipse intersects the major axis called vertices, denoted as V1 and V2. The length of the segment V1V2 is equal 2a. PropertiesofEllipse π1 π2 2π π
- 12. The midpoint of the segment V1V2 is called the center of the ellipse, denoted by C. PropertiesofEllipse π1 π2 πΆ
- 13. The line segment through the center perpendicular to the major axis is the minor axis, denoted as B1B2 which are the covertices. The length of the line segment is equal to 2b. PropertiesofEllipse π1 π2 πΆ π΅1 π΅2 2π π
- 14. The length of the line segment F1F2 is 2c. The line segment through F1 and F2 are called the latera recta and each has a length of 2π2 π . PropertiesofEllipse π1 π2 πΆ π΅1 π΅2 πΉ1 πΉ2 2π π
- 15. The length of the line segment F1F2 is 2c. The line segment through F1 and F2 are called the latera recta and each has a length of 2π2 π . PropertiesofEllipse π1 π2 πΆ π΅1 π΅2 πΉ1 πΉ2 2π2 π π2 π πΈ1 πΈ2 πΈ3 πΈ4
- 16. In ellipse, a>b a>c If a=b, then the ellipse is circle. π2 = π2 β π2 PropertiesofEllipse π1 π2 πΆ π΅1 π΅2 πΉ1 πΉ2 πΈ1 πΈ2 πΈ3 πΈ4
- 17. Definition of Ellipse An ellipse is a set of points such that the sum of the distances from two fixed points is constant. The fixed points are the foci, and the constant sum is the length of major axis. ELLIPSE F F P(x,y) π1 π2 π1 + π2 = ππππ π‘πππ‘ 2π
- 18. GENERALFORMANDFORMULAS π¨ππ + πͺππ + π«π + π¬π + π = π GeneralformofanEllipseequation whereinBismissing,andthe numericalcoefficientsofπ₯2 andπ¦2 havethesamesigns.
- 20. LETβSPRACTICE ππ 36 + ππ 18 = π ππ 4 + ππ 16 = π WHATISππ? ππ?
- 21. EXAMPLE1 Sketch the graph and determine the coordinates of the foci, vertices, and covertices ππ π0 + ππ 36 = π
- 22. EXAMPLE 2 Sketch the graph and determine the coordinates of the foci, vertices, and covertices ππππ + πππ = πππ
- 23. EXAMPLE 3 Find and graph the equation of the ellipse a which satisfies the following conditions: Foci at (Β±2,0); one vertex at (4,0)
- 24. EXAMPLE4 Sketch the graph and determine the coordinates of the foci, vertices, and covertices ππ 9 + ππ 16 = π
- 25. ACTIVITY5 A. Sketch the graph and determine the coordinates of the foci, vertices, and covertices of this ellipse. π₯2 16 + π¦2 25 = 1 B. Determine the standard form of equation of an ellipse given: Vertices (0, Β±5); minor axis of length 6
- 26. ASSESSMENT
- 27. π β π π ππ + π β π π ππ = π π β π π ππ + π β π π ππ = π VERTEXAT(h,k)
- 28. EXAMPLE1 Give the coordinates of the foci, vertices, and covertices (π + 3)π π4 + (π β 5)π 4π = π
- 29. EXAMPLE1 Give the coordinates of the foci, vertices, and covertices of the given general form of ellipse. πππ + ππππ β ππππ + πππ = ππ
- 30. EXAMPLE1 The foci of an ellipse are (β3,β6) and (β3, 2). For any point on the ellipse, the sum of its distances from the foci is 14. Find the standard equation of the ellipse and give the coordinates of the center, vertices and covertices.
- 31. ASSIGNMENT
Editor's Notes
- Always remember, the major axis contains the center, the foci, and the vertices.
- Balik sa definition. The sum of the focal distances of any point on the ellipse is constant and that is equal to 2a. (PF1 + PF2 = 2a)
- Optional. Pwedeng isang at origin or isang hk
- Optional. Pwedeng isang at origin or isang hk