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Ellipse - Graphing

Ellipse - Graphing. Recall that the two equations for the ellipse are given by . Horizontal Ellipse. Vertical Ellipse. Horizontal Ellipse. Vertical Ellipse. Ellipse - Graphing. The center of the ellipse is located at the point (h, k) . Example 1: Determine the center of

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Ellipse - Graphing

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  1. Ellipse - Graphing • Recall that the two equations for the ellipse are given by ... Horizontal Ellipse Vertical Ellipse

  2. Horizontal Ellipse Vertical Ellipse Ellipse - Graphing • The center of the ellipse is located at the point (h, k) ... • Example 1: • Determine the center of • the ellipse given by ... • The center is at C(-4, 3). Slide 2

  3. Horizontal Ellipse Vertical Ellipse Ellipse - Graphing • Note how the position of the a and b switch when changing from the horizontal to the vertical ellipse ... • In the equations for the ellipse, a is always greater than b, or a  b. When the a is under the x, the ellipse is horizontal. When the a is under the y, the ellipse is vertical. Slide 3

  4. Horizontal Ellipse Vertical Ellipse a a Ellipse - Graphing • The vertices of the ellipse are a units from the center and are located on the major axis. Slide 4

  5. Ellipse - Graphing • Two other points on the ellipse can be found at the ends of the minor axis, which is perpendicular to the major axis. • Each of these points is b units from the center. Slide 5

  6. Ellipse - Graphing • The foci lie on the major axis and are c units from the center where ... • Summary: The center is at C(h, k). The vertices are a units from the center on the major axis. Two other points on the ellipse can be found b units from the center on the minor axis. The foci are c units from the center on the major axis. Slide 6

  7. Ellipse - Graphing • Example 2: • Sketch the graph of the • ellipse ... • The center is C(2, -5) • Since 16 4, the a is under the x and the b is under the y. Thus the ellipse is horizontal and ... • The value of c is given by ... Slide 7

  8. 2 -3 3 6 -2 -5 E (2, - 3) -8 C (2, - 5) V (- 2, - 5) V (6, - 5) F (2–23, - 5) E (2, - 7) F (2+23, - 5) Ellipse - Graphing • End points of the minor axis are b = 2 units from the center ... • Use the four points as a guide in drawing the ellipse ... • The foci are c = 23 units from the center on the major axis ... • Center (2, -5) ... • Vertices a= 4 units from the center ... Slide 8

  9. Ellipse - Graphing END OF PRESENTATION Click to rerun the slideshow.

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