The Concept of Eccentricity (Precalculus / Conic Sections / Lesson 8) скачать в хорошем качестве

The Concept of Eccentricity (Precalculus / Conic Sections / Lesson 8)

In this lesson, we learn two definitions of the eccentricity of a conic (and in particular, an ellipse): 1. Eccentricity is the ratio (distance from point to focus)/(distance from point to directrix). 2. Eccentricity is the ratio (distance from center to focus) / (distance from center to endpoint of major axis) We show why these are equivalent definitions, and get intuition and practice. 0:00 Introduction and two earlier perspectives on ellipses 0:40 A new perspective on ellipses (focus/directrix) 2:10 Task 1 (Writing an equation for an ellipse using the focus/directrix) 2:47 Check 1 3:34 Graphing the result from Check 1 5:08 Two definitions of eccentricity 7:07 Proving the two definitions are equal 8:02 Task 2 (Ellipse review / Using the c/a or c/b eccentricity definition) 9:08 Check 2 11:18 Summary 11:59 Appendix 1 (sqrt(x^2) ≠ x when x is negative) 12:50 Appendix 2 (The missing algebraic steps in the proof that the two eccentricity definitions were equivalent)