ELLIPSE-INTRODUCTION.Mathematics- precalcus

Mathematics

1. ELLIPSE

2. Objectives: At the end of the lessons students’ will be able to : 2020 Marketing Agenda H alerdon Real Estate 1.define an ellipse and name its parts accurately; 2.enumarate the properties of ellipse;and 3Write the equations of ellipses with axes coinciding with the coordinate axes.

3. ELLIPSE An ellipse is a set of all points in a plane such that the sum of their distance from two fixed points is constant . FOCI (F1,F2)-two fixed points inside the ellipse

4. ELLIPSE

5. The ellipse is a conic whose eccentricity is less than 1 . ELLIPSE

6. ELLIPSE H alerdon Real Estate

7. ELLIPSE

8. ELLIPSE H alerdon Real Estate

9. Properties of Ellipse 1.The ellipse is a closed curved and is symmetrical with respect both its axes. 2.The sum of the focal distances of any point on the ellipse is constant and equal to the legn th of the major axis: PF 1 +PF 2 = 2a

10. Properties of Ellipse 2020 Marketing Agenda 3. As a corollary to the preceding property, we see that the di st ance from a focus to a vertex at one end of the minor axis is equal to half the length of the major axis: F/V: a,

11. Properties of Ellipse H alerdon Real Estate 4.The distances from the center to a focus and to a directrix are respectively ae and a/e

12. Properties of Ellipse H alerdon Real Estate Eccentricity,  e c a   e =

13. Properties of Ellipse H alerdon Real Estate 4.The distances from the center to a focus and to a directrix are respectively ae and a/e

14. Properties of Ellipse 2020 Marketing Agenda H alerdon Real Estate 5.The length of latus rectum is 2b ² /a.

15. H alerdon Real Estate Equation of Ellipse with its axes coinciding the Coordinate

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17. H alerdon Real Estate d 1=the distance from (− c ,0) to ( x , y ) d 2=the distance from ( c ,0) to ( x , y )

18. H alerdon Real Estate Thus, the standard equation of an ellipse is  . This equation defines an ellipse centered at the origin. If  a > b , the ellipse is stretched further in the horizontal direction, and if  b > a , the ellipse is stretched further in the vertical direction.

19. Le t's pave the way! Let's work towards greater heights in 2021. 2020 Marketing Agenda H alerdon Real Estate