conic sections advanced geometry conic sections lesson 2

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Conic Sections Advanced Geometry Conic Sections Lesson 2

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Page 1: Conic Sections Advanced Geometry Conic Sections Lesson 2

Conic Sections

Advanced GeometryConic Sections

Lesson 2

Page 2: Conic Sections Advanced Geometry Conic Sections Lesson 2

Conic SectionsA curve determined by the intersection of a plane

with a double right cone.

Circle Ellipse Hyperbola Parabola

Page 3: Conic Sections Advanced Geometry Conic Sections Lesson 2

Axis of Symmetry

DirectrixVertex

Focus

Parabola

Page 4: Conic Sections Advanced Geometry Conic Sections Lesson 2

VerticalAxis of Symmetry

Horizontal Axis of Symmetry

Page 5: Conic Sections Advanced Geometry Conic Sections Lesson 2

Example:Using the graphs below, provide all of the listed information.

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Page 6: Conic Sections Advanced Geometry Conic Sections Lesson 2

Ellipse

Center

Major Axis

Minor Axis

Vertices Foci

Page 7: Conic Sections Advanced Geometry Conic Sections Lesson 2

VerticalMajor Axis

HorizontalMajor Axis

Page 8: Conic Sections Advanced Geometry Conic Sections Lesson 2

Example:Using the graphs below, provide all of the listed information.

Center:

Foci:

Length of theMajor Axis:

Length of theMinor Axis:

Vertices:

Page 9: Conic Sections Advanced Geometry Conic Sections Lesson 2

Hyperbola

Center

Foci

Transverse Axis

Conjugate Axis

Vertices

Asymptotes

Page 10: Conic Sections Advanced Geometry Conic Sections Lesson 2

VerticalTransverse Axis

HorizontalTransverse Axis

Page 11: Conic Sections Advanced Geometry Conic Sections Lesson 2

Example:Using the graphs below, provide all of the listed information.

Center:

Vertices:

Foci:

Slopes of theAsymptotes:

Page 12: Conic Sections Advanced Geometry Conic Sections Lesson 2

Example:Graph the specified conic section using the information provided.

Ellipse

Center: (-3,0)

Foci: (8, -3)

Length of theMajor Axis: 20 units

Length of theMinor Axis: 12 units

Vertices: (10, -3), (0, 3), (0, -9)

Page 13: Conic Sections Advanced Geometry Conic Sections Lesson 2

Parabola

Vertex: (1, 1)

Focus: (4, 1)

Axis of Symmetry: y = 1

Directrix: x = -2

Example:Graph the specified conic section using the information provided.

Page 14: Conic Sections Advanced Geometry Conic Sections Lesson 2

Circle

Center: (-3,-3)

Radius: 6 units

Example:Graph the specified conic section using the information provided.

Page 15: Conic Sections Advanced Geometry Conic Sections Lesson 2

Hyperbola

Center: (2, -1)

Vertices: (2, 3), (2, -5)

Foci: (2, 4), (2, -6)

Slopes of theAsymptotes:

Example:Graph the specified conic section using the information provided.

4

3m