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.