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: 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.

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.)

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

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.

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.

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

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

**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)

**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)

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