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10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
10.4 ellipses
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10.4 ellipses

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  • 1. Definition of an Ellipse Set of all points P such that the sum of thedistances between P and the two foci (pluralfor “focus”) is constant.d1 + d2 = constant
  • 2. Characteristics of Ellipses
  • 3. Standard form Ellipse Equation: a > b > 0The foci are on the major axis, c units from thecenter, where c2 = a2 – b2Equation Major Axis Vertices Co-VerticesHorizontal ( a, 0) (0, b)Vertical (0, a) ( b, 0)
  • 4. Graphing1. Write in standard form.2. Use a and b to plot vertices and co-vertices.3. Draw the ellipse connecting all 4 points.Example:Draw the ellipse given byand identify the foci.
  • 5. Your Turn! Graph and identify the foci.
  • 6. Writing Equations Write an equation of the ellipse with the givencharacteristics and center (0, 0). Vertex: (0, 7)Co-Vertex: (-6, 0) Vertex: (-4, 0)Focus: (2, 0)
  • 7. Your Turn! Write an equation of the ellipse with center(0,0) and: vertex at (3, 0) co-vertex at (0, -1)
  • 8. Area of an Ellipse A = πabExample:A portion of the White House lawn is called TheEllipse. It is 1060 feet long and 890 feet wide.1. Write an equation of The Ellipse.2. Find the area of The Ellipse.
  • 9. Modeling with an Ellipse In it’s elliptical orbit, Mercury ranges from46.04 million km to 69.86 million km from thecenter of the sun, which is a focus of theorbit. Write an equation of the orbit.

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