Objective Understand identify basic characteristics of conics Conic

Objective: Understand 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.

Parabola (Conical Definition): ________ 9. 1 Parabolas 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. The line passing through the focus and the vertex. (h, k)

Standard form If the axis is ___________ (x is squared): of the equation of a parabola with vertex at (h, k) p is 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: _____

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

**Determine Characteristics and sketch graphs** Given the equation of a parabola, identify its a. b. c. d. Vertex Focus 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. b. c. d. Vertex Focus 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.