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Ellipse - Finding the Equation

Ellipse - Finding the Equation. Recall that the two equations for the ellipse are given by. Horizontal Ellipse. Vertical Ellipse. Ellipse - Finding the Equation. Summary of meanings of a, b, h, and k:. The center is at C(h, k).

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Ellipse - Finding the Equation

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

  2. Ellipse - Finding the Equation • Summary of meanings of a, b, h, and k: The center is at C(h, k). The vertices are a units from the center on the major axis. The end points of the minor axis are b units from the center. The foci are c units from the center on the major axis. Slide 2

  3. Ellipse - Finding the Equation • Example 1: • Find the equation of the ellipse with the given vertices • and foci ... • The first step is to plot these points on a coordinate plane. Slide 3

  4. Ellipse - Finding the Equation • The center will be the midpoint of the line segment joining the vertices (also the foci) ... • The distance from the center to a vertex is a = 6. • The distance from the center to a focus is c = 4. Slide 4

  5. Ellipse - Finding the Equation • Using the formula ... the value of b can be found. Slide 5

  6. Ellipse - Finding the Equation • Summary: • Since the vertices are vertical, the ellipse is vertical ... and the equation is ... Slide 6

  7. Ellipse - Finding the Equation • Example 2: • Find the standard form of the ellipse given by ... • Solution: Slide 7

  8. Ellipse - Finding the Equation • The standard form of the ellipse is ... Slide 8

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

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