Ellipses

1
Ellipses

• 9.3

2
Ellipse

• An ellipse is the collection of all points in the
  plane the sum of whose distances from two fixed
  points, called the foci, is a constant.

3
Ellipse
Major AxisThe line containing the foci. The
foci are the points marked F. The length is the
distance from one vertex to another.
4
Ellipse
V
V
F
F
C
CenterThe midpoint of the line segment joining
the foci.( denoted C in the picture above.)
5
Ellipse
V
V
F
F
C
Minor AxisThe line through the center and
perpendicular to the major axis.
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Ellipse
V
V
F
F
C
Verticespoints of intersection of the ellipse
and the major axis. (labeled v in the picture.)
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Ellipse Facts

• Know the chart on page 669 of the book.
• Note how the ellipse equations look and how they
  compare to the parabola equations.
• If the major axis or longer part of the ellipse
  is parallel to the y-axis, then the a2 is under
  the y2 term.
• If the major axis or longer part of the ellipse
  is parallel to the x-axis, then a2 is under the
  x2 term.

8
Graphing on the Calculatory2

• Example (x-2)2/9 (y3)2/8 1
• Solve for y.
• 1 (x-2)2/9 (y3)2/8
• 8 8(x-2)2/9 (y3)2
• squarerroot(8 8(x-2)2/9 ) y3
• -3 squarerroot(8 8(x-2)2/9 ) y

9
Find the Equation of the Ellipse Described

• 28-38 evens

10
Find the vertex, and focus of each ellipse. Then
graph by hand and by calc.

• Use the chart to help find the two items.
• When graphing, graph the two items and then graph
  the two vertices and the two endpoints of the
  minor axis. Then draw in the ellipse.

11
Write an Equation for a Parabola Given the center
and points on the ellipse.

• Find the correct standard form for the ellipse
  based on how the major axis lies.
• Plug the vertex in for h and k.
• Find a by determining the distance from the
  center to a vertex on the graph.
• Find b by determining the distance from the
  center to the other endpoints of the
  ellipseminor axis.
• Write the equation with the a, b, h, and k
  plugged in, and leave the x and y as x and y.