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CHAPTER 10

- CONICS
- Section 10.3
- Ellipses

Section 10.3 Ellipses

- Reading Quiz (hour 1)
- .

Section 10.3 Ellipses

- Reading Quiz (hour 4)
- .

Section 10.3 Ellipses

- I need three volunteers

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

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

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

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?

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)

Section 10.3 Ellipses

- Example 3

Write the equation of the ellipse in standard

form. Then find the coordinates of its foci.

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.

Section 10.3 Ellipses

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.

Section 10.3 Ellipses

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.

Section 10.3 Ellipses

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.

Section 10.3 Ellipses

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.

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