7.1 video tutorials

8/20/2019 7.1 Video Tutorials

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Lesson 7.1 The Ellipse

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A. Geometric Definition of an Ellipse

B. Ellipse with Center at the Origin

The graph of the equation of each of the following equations is an ellipse with center at the origin andhaving the given properties.

Equation

2 2

2 2 1

0

x y

a b

a b

2 2

2 2 1

0

x y

b a

a b

Vertices ,0a 0, a

Major Axis Horizontal, length 2a Vertical, length 2a

Minor Axis Vertical, length 2b Horizontal, length 2b

Foci 2 2 2,0 ,c c a b 2 2 20, ,c c a b

Graphs

An ellipse is the set of points in the plane the sum of whose distances from

two fixed points F1 and F2 remain constant. These two fixed points are the

foci (plural of focus) of the ellipse.


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C. Ellipse with Center at (h, k )

Find the vertices and foci of the ellipse. Determine the lengths of the major and

minor axes, and sketch the graph.

1.2 2

116 25

x y Video tutorial

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

The graph of the equation of each of the following equations is an ellipse with center at the (h, k ) andhaving the given properties.

Equation

0

12

2

2

2

ba

b

k y

a

h x

0

12

2

2

2

ba

a

k y

b

h x

Vertices ),(and ),( k ahk ah ),(and ),( ak hak h

Major Axis Horizontal, length 2a Vertical, length 2a

Minor Axis Vertical, length 2b Horizontal, length 2b

Foci 222

),( and ),(bac

k chk ch

222),( and ),(

bacck hck h

http://www.youtube.com/watch?v=9fp5Poz-xh0&hd=1http://www.youtube.com/watch?v=9fp5Poz-xh0&hd=1http://www.youtube.com/watch?v=9fp5Poz-xh0&hd=1


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2. 2 24 16 x y Video tutorial

3. 2 24 25 100 x y Video tutorial

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=cg7tDKeJh7w&hd=1http://www.youtube.com/watch?v=cg7tDKeJh7w&hd=1http://www.youtube.com/watch?v=xUnIaTFsJXg&hd=1http://www.youtube.com/watch?v=xUnIaTFsJXg&hd=1http://www.youtube.com/watch?v=xUnIaTFsJXg&hd=1http://www.youtube.com/watch?v=cg7tDKeJh7w&hd=1


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Find the equation for each ellipse. Graph the equation.

4. Center at (0, 0); focus at (-1, 0); vertex at (3, 0) Video tutorial

Equation:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=O8odbcv3q9U&hd=1http://www.youtube.com/watch?v=O8odbcv3q9U&hd=1http://www.youtube.com/watch?v=O8odbcv3q9U&hd=1


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Find the equation for each ellipse. Graph the equation.

5. Foci at (0, ± 2); length of major axis is 8 video tutorial

Equation:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=OiRaxSELB7w&hd=1http://www.youtube.com/watch?v=OiRaxSELB7w&hd=1http://www.youtube.com/watch?v=OiRaxSELB7w&hd=1


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Write and equation for the ellipse. Video tutorial

6.

http://www.youtube.com/watch?v=688l4dvpfTo&hd=1http://www.youtube.com/watch?v=688l4dvpfTo&hd=1http://www.youtube.com/watch?v=688l4dvpfTo&hd=1


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Analyze each equation; that is, find the center, foci, and vertices of each ellipse.

Graph each equation.

7.

14

2

9

422

y x

Video tutorial

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=oR8HeERlkmY&hd=1http://www.youtube.com/watch?v=oR8HeERlkmY&hd=1http://www.youtube.com/watch?v=oR8HeERlkmY&hd=1


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8. 09123 22 y y x Video tutorial

Equation:

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=tHk6qru46LQ&hd=1http://www.youtube.com/watch?v=tHk6qru46LQ&hd=1http://www.youtube.com/watch?v=tHk6qru46LQ&hd=1


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9. 56834 22 y x y x Video tutorial

Equation:

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=NJlp6Jr5dgg&hd=1http://www.youtube.com/watch?v=NJlp6Jr5dgg&hd=1http://www.youtube.com/watch?v=NJlp6Jr5dgg&hd=1


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Find an equation for each ellipse. Graph the equation.

10. Center at (-3,1); vertex at (-3, 3); focus at (-3, 0) Video tutorial

Equation:

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=ckjln0Ug8qg&hd=1http://www.youtube.com/watch?v=ckjln0Ug8qg&hd=1http://www.youtube.com/watch?v=ckjln0Ug8qg&hd=1


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11. Foci at (1, 2) and (-3, 2); vertex at (-4, 2) Video tutorial

Equation:

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=UzhPSJQHRZ0&hd=1http://www.youtube.com/watch?v=UzhPSJQHRZ0&hd=1http://www.youtube.com/watch?v=UzhPSJQHRZ0&hd=1


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Video tutorial 12. Center at (1, 2); focus at (1, 4); contains the point (2, 2).

Equation:

Center:

Vertices:

Major axis:

Minor axis:

What’s c?

Foci:

http://www.youtube.com/watch?v=FCnPTFCpO3c&hd=1http://www.youtube.com/watch?v=FCnPTFCpO3c&hd=1http://www.youtube.com/watch?v=FCnPTFCpO3c&hd=1


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13. Semielliptical Arch BridgeA bridge is built in the shape of a semielliptical arch. The bridge has a span of

120 feet and a maximum height of 25 feet. Choose a suitable rectangular

coordinate system and find the height of the arch at 10 feet from the center.

Video tutorial

http://www.youtube.com/watch?v=nBZb9i6wCH4&hd=1http://www.youtube.com/watch?v=nBZb9i6wCH4&hd=1


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14. Whispering GalleryThe whispering gallery in the Museum of Science and Industry in Chicago is 47.3

feet long. The distance from the center of the room to the foci is 20.3 feet. Find

an equation that describes the shape of the room. How high is the room at its

center?

Video tutorial
http://www.youtube.com/watch?v=K_Knz4nXDbs&hd=1http://www.youtube.com/watch?v=K_Knz4nXDbs&hd=1http://www.youtube.com/watch?v=K_Knz4nXDbs&hd=1

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