March 19 th copyright2009merrydavidson Conic sections.

Slides:

Advertisements

Similar presentations

Conic Sections Parabola.

Advertisements

Today in Precalculus Notes: Conic Sections - Parabolas Homework

Section 11.6 – Conic Sections

What do we know about parabolas?. Conic Slice Algebraic Definition Parabola: For a given point, called the focus, and a given line not through the focus,

Math 143 Section 7.3 Parabolas. A parabola is a set of points in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the.

Unit 5 Conics... The parabola is the locus of all points in a plane that are the same distance from a line in the plane, the directrix, as from a fixed.

Colleen Beaudoin For FCIT.  Review: The geometric definition relies on a cone and a plane intersecting it.  Algebraic definition: All points that are.

Parabolas Date: ____________.

Parabolas Definitions Parabola – set of all points equidistant from a fixed line (directrix) and a fixed point (focus) Vertex – midpoint of segment from.

INTRO TO CONIC SECTIONS. IT ALL DEPENDS ON HOW YOU SLICE IT! Start with a cone:

Sullivan Algebra and Trigonometry: Section 10.2 The Parabola

Section 7.1 – Conics Conics – curves that are created by the intersection of a plane and a right circular cone.

11.4 The Parabola. Parabola: the set of all points P in a plane that are equidistant from a fixed line and a fixed point not on the line. (directrix)

Conic Sections Parabola. Conic Sections - Parabola The intersection of a plane with one nappe of the cone is a parabola.

Chapter 9 Analytic Geometry.

Unit 1 – Conic Sections Section 1.3 – The Parabola Calculator Required Vertex: (h, k) Opens Left/RightOpens Up/Down Vertex: (h, k) Focus: Directrix: Axis.

ALGEBRA 2 Write an equation for a graph that is the set of all points in the plane that are equidistant from point F(0, 1) and the line y = –1. You need.

Review Day! Hyperbolas, Parabolas, and Conics. What conic is represented by this definition: The set of all points in a plane such that the difference.

10.2 Parabolas JMerrill, Review—What are Conics Conics are formed by the intersection of a plane and a double-napped cone. There are 4 basic conic.

Section 10.1 Parabolas Objectives: To define parabolas geometrically.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

9.2 Notes – Parabolas.

Warm Up Parabolas (day two) Objective: To translate equations into vertex form and graph parabolas from that form To identify the focus, vertex,

Conics can be formed by the intersection

10.2 The Parabola. A parabola is defined as the locus of all points in a given plane that are the same distance from a fixed point, called the focus,

9.2 THE PARABOLA. A parabola is defined as the collection of all points P in the plane that are the same distance from a fixed point F as they are from.

10.2 The Parabola. A parabola is defined as the collection of all points P in the plane that are the same distance from a fixed point F as they are from.

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Copyright © 2011 Pearson Education, Inc. The Parabola Section 7.1 The Conic Sections.

10.2 Introduction to Conics: Parabola General Equation of all Conics Latus rectum.

Section 11.1 Section 11.2 Conic Sections The Parabola.

Section 9.3 The Parabola. Finally, something familiar! The parabola is oft discussed in MTH 112, as it is the graph of a quadratic function: Does look.

April 18, 2012 Conic Sections Intro - Parabola Warm-up: Write the quadratic equation in vertex form and identify the vertex. 1.y = x 2 – 6x y =

Section 10-2 Pages Introduction to Conics: Parabolas.

Advanced Geometry Conic Sections Lesson 3

Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2.

Parabola  The set of all points that are equidistant from a given point (focus) and a given line (directrix).

Conic Sections.

Conic Sections The Parabola. Introduction Consider a ___________ being intersected with a __________.

Conics: Parabolas. Parabolas: The set of all points equidistant from a fixed line called the directrix and a fixed point called the focus. The vertex.

10.2 Parabolas. Objective To determine the relationship between the equation of a parabola and its focus, directrix, vertex, and axis of symmetry. To.

Introduction to Conic Sections Conic sections will be defined in two different ways in this unit. 1.The set of points formed by the intersection of a plane.

Conic Sections There are 4 types of Conics which we will investigate: 1.Circles 2.Parabolas 3.Ellipses 4.Hyperbolas.

Distance The distance between any two points P and Q is written PQ. Find PQ if P is (9, 1) and Q is (2, -1)

Warm UpNO CALCULATOR 1) Determine the equation for the graph shown. 2)Convert the equation from polar to rectangular. r = 3cosθ + 2sin θ 3)Convert the.

INTRO TO CONIC SECTIONS. IT ALL DEPENDS ON HOW YOU SLICE IT! Start with a cone:

10.5 Parabolas Objective: Use and determine the standard and general forms of the equations of a parabolas. Graph parabolas.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

Thursday: Announcements

10.1 Circles and Parabolas Conic Sections

10.1 Parabolas.

Warm Up circle hyperbola circle

Ch10.2 and additional material

Unit 2: Day 6 Continue .

Conic Sections Parabola.

Focus of a Parabola Section 2.3.

Chapter 6: Analytic Geometry

GSE Pre-Calculus Keeper 10

Warm-up: Complete the square: HW: pg803 (8 – 20 even, 30 – 50 even)

Write an equation of a parabola with a vertex at the origin and a focus at (–2, 0). [Default] [MC Any] [MC All]

Parabola Last Updated: October 11, 2005.

Conic Sections The Parabola.

Section 11.6 – Conic Sections

Intro to Conic Sections

5.1 Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Conic Sections - Parabolas

5.1 Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Objectives & HW Students will be able to identify vertex, focus, directrix, axis of symmetry, opening and equations of a parabola. HW: p. 403: all.

Presentation transcript:

March 19 th copyright2009merrydavidson Conic sections

Conic Sections A conic section is the intersection of a plane and a double cone.

Parabolas A Parabola is the set of all points in a plane that are equidistant between a fixed point (focus) and a line (directrix).

y = a(x – h) 2 + k focus directrix Axis of symmetry focal chord (h,k) When “a” is positive, it opens UP When “a” is negative, it opens DOWN

Where to find them… FOCUS: inside the parabola DIRECTRIX: outside of the parabola AOS: through the vertex, perpendicular to the directrix FOCAL CHORD (latus rectum): inside of the parabola

The distance from the vertex to the focus and the vertex to the directrix are equal. Length of the focal chord is

When graphing you MUST label… vertex focus directrix axis of symmetry focal chord

Ex 1:y = (x +1) Vertex Opens AOS a = focal pt. end points of LR (-1,5) down x = -1 8 (-1,3) (3,3) & (-5,3) directrix y = 7

Steps to graph: 1)Plot the vertex. 2)Find/graph the AOS 2) Find “p”. 3) Count “p” units above the vertex and “p” units below the vertex for the focus and directrix. 4) Draw in and label the focus and directrix. 5) Calculate. Go HALF that many units to the right and left of the focus. These are the end points of the focal chord. Draw in the focal chord. 6) Now you know the stretch of the parabola, draw it in.

Ex 2: Vertex Opens AOS a =focal pt. directrix end points of LR (-7,3) up y = 2 x = -7 (-7,4) (-6,4) & (-9,4)

Ex 3a)Find the equation of the parabola with focus at (-3,-2) and THE DIRECTRIX at y = -6 Graph what you know. How far is it from the focus to the directrix? 4 Find the vertex and graph it. (-3, -4) Find “a”. directrix

Ex 4: Given the focus at (0,5) and the vertex at (0,1); write the equation.

Parabolas

x = a(y – k) 2 + h directrix focus Axis of symmetry focal chord (h,k) When “a” is positive, it opens RIGHT When “a” is negative, it opens LEFT

Vertex Opens AOS a =focus directrix endpoints of LR Ex 5: x = (y + 4) (-1,- 4) right y = - 4 (2,- 4) x = - 4 (2,2),(2,-10)

Ex 6: x = - 3(y + 1) Vertex Opens AOS a =focus directrix endpoints of LR (-3, -1) left y = -1

Ex 7a)Find the equation of the parabola with focus at (4,0) and THE DIRECTRIX at x = -2 Graph what you know. How far is it from the focus to the directrix? 6 Find the vertex and graph it. (1, 0) Find “a”. directrix

Ex 8: Change to vertex form:y = x 2 + 6x + 3

Ex 9: Given a graph, write the equation.

HW: WS 10-1