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Review Day! Hyperbolas, Parabolas, and Conics

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What conic is represented by this definition: The set of all points in a plane such that the difference of the distances between and two distinct fixed points (the foci) is a constant.

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Hyperbola A hyperbola is the set of all points in a plane such that the difference of the distances between and two distinct fixed points (the foci) is a constant.

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What conic is represented by this definition: An open curve formed by the intersection of a double napped cone and a plane that is not parallel or perpendicular to the axis of the cone.

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Parabola An open curve formed by the intersection of a double napped cone and a plane that is not parallel or perpendicular to the axis of the cone.

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What conic is represented by this definition: An open curve formed by the intersection of a double napped cone and a plane that is perpendicular to the base of the cone (parallel to axis of cone).

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Hyperbola An open curve formed by the intersection of a double napped cone and a plane that is perpendicular to the base of the cone (parallel to axis of cone).

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What conic is represented by this definition: The set of all points that are equidistant from a fixed line (the directrix) and a fixed point (the focus) not on the line.

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Parabola The set of all points that are equidistant from a fixed line (the directrix) and a fixed point (the focus) not on the line.

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What conic is represented by this definition: The set of all points in a plane that are a fixed distance, called the radius, from a fixed point, called the center.

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Circle The set of all points in a plane that are a fixed distance, called the radius, from a fixed point, called the center.

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What conic is represented by this definition: A closed curve formed by the intersection of a double napped cone and a plane perpendicular to the axis of the cone. (parallel to the base of the cone)

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Circle A closed curve formed by the intersection of a double napped cone and a plane perpendicular to the axis of the cone. (parallel to the base of the cone)

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What conic is represented by this definition: The set of all points in a plane such that the sum of the distances between and two distinct fixed points (the foci) is a constant.

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Ellipse The set of all points in a plane such that the sum of the distances between and two distinct fixed points (the foci) is a constant.

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What conic is represented by this definition: A closed curve formed by the intersection of a double napped cone and a plane that is not parallel or perpendicular to the axis of the cone

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Ellipse A closed curve formed by the intersection of a double napped cone and a plane that is not parallel or perpendicular to the axis of the cone

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What conic section does this equation represent:

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Hyperbola

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What conic section does this equation represent:

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Parabola

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What conic section does this equation represent:

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Hyperbola

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What conic section does this equation represent:

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Hyperbola

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What conic section does this equation represent:

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Ellipse

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What conic section does this equation represent:

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Ellipse

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What conic section does this equation represent:

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Circle

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Write the Equation for this… Hyperbola Vertices at (-2, 1) and (-2, 11) Foci at (-2, 0) and (-2, 12)

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Hyperbola Vertices at (-2, 1) and (-2, 11) Foci at (-2, 0) and (-2, 12)

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Write the Equation for this… Parabola Vertex (4, 8) Focus (4, 6)

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Parabola Vertex (4, 8) Focus (4, 6)

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Write the Equation for this… Hyperbola Vertices (-6, 1) and (2, 1) Slopes of the asymptotes:

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Hyperbola Vertices (-6, 1) and (2, 1) Slopes of the asymptotes:

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True or False? If the.. Focus (-2, 0) and the directrix is x= -6, The parabola opens left.

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False If the.. Focus (-2, 0) and the directrix is x=-6… The parabola opens left.

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True or False? If the.. Vertex is at (1, 4) and the focus is at (1, 5).. The focal width is 5.

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False If the.. Vertex is at (1, 4) and the focus is at (1, 5).. The focal width is 5.

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Also Study: Graphing Hyperbolas & Parabolas How to find the equation of the asymptotes (see Hyperbola day #1 notes) Check out p 755 #13 and #35!

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