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Ellipse Equations: Center, Vertices, and Foci

Learn how to find the equation of an ellipse by understanding its key components such as center, vertices, and foci. Follow examples to grasp the process step by step.

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Ellipse Equations: Center, Vertices, and Foci

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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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