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Vertex

Ch. 9. Objective: Understand and identify basic characteristics of conics. Conic section (conic): What you get (the intersection)when you cross a plane and a double-napped cone. 4 Basic Conics:. Vertex. Axis. ELLIPSE:

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Vertex

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  1. Ch. 9 Objective: Understand and identify basic characteristics of conics. Conic section (conic): What you get (the intersection)when you cross a plane and a double-napped cone. 4 Basic Conics: Vertex Axis

  2. ELLIPSE: The plane is slightly tilted so it’s no longer perpendicular to the axis. CIRCLE: The plane is exactly perpendicular to the cone’s axis.

  3. PARABOLA: Keep tilting so that the plane is now exactly parallel to the side of the top cone. (Parabola occurs because one side of the ellipse sort of falls off.)

  4. HYPERBOLA: Keep tilting so that the plane is now slicing though both the top and bottom parts of the cone.

  5. CONICS (Pre/Calc Style): Conic: A __________________of points satisfying a certain geometric property. Ex: A circle is the locus of all points equidistant from a fixed center point.

  6. 9.1 Parabolas Parabola (Conical Definition): The set of all points (x, y) in a plane that are __________ from a fixed line, the _______(parallel to the x or y-axis), and a fixed point (not on the line), called the _________. ________ The midpoint between the focus and the directrix. (h, k) ________ The line passing through the focus and the vertex.

  7. If the axis is _____________________ (x is squared): Standard form of the equation of a parabola with vertex at (h, k) pis the ____________________(can be positive or negative) from the vertex to the focus Note: p≠0 V F F V P _______ P _____ Vertex: ___________ Focus: ___________ Axis of Symmetry: ________ Directrix: __________

  8. Standard form of the equation of a parabola with vertex at (h, k) If the axis is ________________ __________(y is squared) p is the directed distance (can be positive or negative) from the vertex to the focus Note: p≠0 V F F V P _____ P _____ Vertex: ___________ Focus: ___________ Axis of Symmetry: _________ Directrix: _________

  9. **Determine Characteristics and sketch graphs** Given the equation of a parabola, identify its a. Vertex b. Focus c. Axis of symmetry Directrix Hint: Determine orientation of the parabola and p first. Ex. 1)

  10. **Determine Characteristics and sketch graphs** Given the equation of a parabola, identify its a. Vertex b. Focus c. Axis of symmetry Directrix Hint: Determine orientation of the parabola and p first. Ex. 2)

  11. HW : For each parabolic equation, identify (and sketch) the parabola’s : a) Vertex b) Focus c) Axis of symmetry d) Directrix.

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