CONICS

1
CHAPTER 10

• CONICS
• Section 10.3
• Ellipses

2
Section 10.3 Ellipses

• Reading Quiz (hour 1)
• .

3
Section 10.3 Ellipses

• Reading Quiz (hour 4)
• .

4
Section 10.3 Ellipses

• I need three volunteers

5
Section 10.3 Ellipses

• Ellipse
• Major axis
• Semi-major axis (a)
• Minor axis
• Semi-minor axis (b)
• Center
• Vertices
• Foci (c units
• from center)

The foci are on the major axis
6
Section 10.3 Ellipses

• There is an important relationship between the
  lengths of a, b, and c
• a2 b2 c2
• a length of semi-major
• b length of
• semi-minor
• c length from
• center to foci

7
Section 10.3 Ellipses

• Here is another important relationship between
  the lengths
• e c/a
• a length of semi-major
• c length from
• center to foci
• e eccentricity
• shape of the
• ellipse

8
Section 10.3 Ellipses

• Example 1 Landscape Architecture
• The ellipse in Washington, D.C., is an
  elliptical grassy area between the White House
  and the Washington Monument. Its major axis is
  approximately 500 yards and its minor axis is
  approximately 425 yards. How far apart are the
  foci?

9
Section 10.3 Ellipses

• Example 2
• Consider the graphed ellipse.
• Write the equation of the ellipse in standard
  form.
• Find the coordinates of the foci.

(7,1)
(3,1)
(3,-4)
10
Section 10.3 Ellipses

• Example 3

Write the equation of the ellipse in standard
form. Then find the coordinates of its foci.
11
Section 10.3 Ellipses

• Example 4
• For the equation
• ² ²1

Find the coordinates of the center, foci and the
vertices of the ellipse. Then graph the
equation.
12
Section 10.3 Ellipses
13
Section 10.3 Ellipses

• Example 5
• The equation of the ellipse is

• Write the standard form of the equation.
• Find the coordinates of the center.
• Find the coordinates of the foci.
• Find the coordinates of the vertices.
• Graph the equation.

14
Section 10.3 Ellipses
15
Section 10.3 Ellipses

• Example 6

Find the coordinates of the center, foci and the
vertices of the ellipse with the equation.
Then graph the equation.
16
Section 10.3 Ellipses
17
Section 10.3 Ellipses

• Example 7
• The eccentricity of Uranus is 0.047. Its orbit
  is about 18.30 AU from the sun at its closest
  point to the sun. The length of the semi-major
  axis of the orbit is about 19.21 AU.
• a. Sketch the orbit of Uranus showing the sun in
  its position.

18
Section 10.3 Ellipses
19
Section 10.3 Ellipses

• Example 7 (cont)
• Find the length of the semi-minor axis of the
  orbit.
• Find the distance of Uranus from the sun at its
  farthest point.