Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes.

Slides:



Advertisements
Similar presentations
Copyright © Cengage Learning. All rights reserved.
Advertisements

Conic Sections: Eccentricity
W RITING AND G RAPHING E QUATIONS OF C ONICS GRAPHS OF RATIONAL FUNCTIONS STANDARD FORM OF EQUATIONS OF TRANSLATED CONICS In the following equations the.
© 2010 Pearson Education, Inc. All rights reserved.
Conics: Standard Form Pre-Calculus Conics part 1.
11.5 Translation of Axes & the General Form. So far our conic sections in general form have looked like this: Ax 2 + Cy 2 + Dx + Ey + F = 0 But there.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 653 Find the vertices and foci of the ellipse.
By: Leonardo Ramirez Pre Calculus Per.6 Mr. Caballero.
Copyright © Cengage Learning. All rights reserved.
NONLINEAR SYSTEMS, CONIC SECTIONS, SEQUENCES, AND SERIES College Algebra.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 682 Find a polar equation for the conic with a.
Copyright © 2011 Pearson, Inc. P.2 Cartesian Coordinate System.
Section 5 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 Second-Degree Inequalities and Systems of Inequalities Graph.
Identifying Conic Sections
Slide Copyright © 2012 Pearson Education, Inc.
8.6 Translate and Classify Conic Sections
Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas. Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Geometry of a Hyperbola Translations.
Rotation of Axes; General Form of a Conic
General Form to Standard Form OR Vertex Form
8.6 Conic Sections Write equations of conic sections in standard form Identify conic sections from their equations.
Rotating Conic Sections
Copyright © 2011 Pearson, Inc. 6.3 Parametric Equations and Motion.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 10 Parametric and Polar Curves.
Chapter 9 Conic Sections and Analytic Geometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Rotation of Axes.
Chapter 10.5 Conic Sections. Def: The equation of a conic section is given by: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 Where: A, B, C, D, E and F are not.

SECTION: 10 – 4 ROTATIONS WARM-UP Find the center, vertices, foci, and the equations of the asymptotes of each hyperbola. 3. Write the standard form of.
Slide Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
10.4 Rotation and Systems of Quadratic Equations.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Solve for y and use a function grapher to graph.
Section 2 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives The Circle and the Ellipse Find an equation of a circle.
Sullivan Algebra and Trigonometry: Section 11.5 Objectives of this Section Identify a Conic Use a Rotation of Axes to Transform Equations Discuss an Equation.
Circles Ellipse Parabolas Hyperbolas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1.
Copyright © 2011 Pearson, Inc. 7.1 Solving Systems of Two Equations.
11.6 Solving Quadratic Systems. Two equations of the form Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 considered together is called a quadratic system. You can.
Conic Sections By: Danielle Hayman Mrs. Guest Per. 4.
Slide Chapter 8 Analytic Geometry in Two and Three Dimensions.
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 9 Analytic Geometry and the Conic Sections.
10.5 Rotation of Conics. The Standard Equation for all Conics Ax 2 + Bxy + Cy 2 + Dx + Ey + F = o So far B has equal zero and all graphs have been horizontal.
Copyright © Cengage Learning. All rights reserved. 9.3 Hyperbolas and Rotation of Conics.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Using the point P(x, y) and the rotation information,
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.4 Translations and Rotations of Axes.
Tilted Conics 1.Use the discriminant to classify conics. 2.Rotate the coordinate axes to eliminate the xy term in equations of conics. 1.
Copyright © 2011 Pearson Education, Inc. The Parabola Section 7.1 The Conic Sections.
Section 9.1 Quadratic Functions and Their Graphs.
Notes Over 10.6 Writing an Equation of a Translated Parabola Write an equation for the parabola.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Solve a system of equations containing first- or second-degree equations in.
Section 8.5. In fact, all of the equations can be converted into one standard equation.
Chapter 8 Part 2 Sections 8-4, 8-5, & 8-6. Section 8-4  solve for y and graph in a calculator  rotating a point (use formulas)  find the angle of rotation.
W RITING AND G RAPHING E QUATIONS OF C ONICS GRAPHS OF RATIONAL FUNCTIONS STANDARD FORM OF EQUATIONS OF TRANSLATED CONICS In the following equations the.
Warm Up. Some rules of thumb for classifying Suppose the equation is written in the form: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0, where A – F are real coefficients.
Rotation of Axis.
Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola.
Copyright © 2011 Pearson, Inc. 2.7 Solving Equations in One Variable.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter 10 Review MTH 253 – Calculus. Conics and Quadratic Equations Conics Parabola Ellipse Circle Hyperbola.
Copyright © 2004 Pearson Education, Inc. 1 Notes #3-___ Date:______ Vertex Nappes (the two cones) Generator Axis 8.1 Introduction to Conics: Parabolas.
Classifying Conic Sections
Differential Equations
© 2010 Pearson Education, Inc. All rights reserved
Classifying Conic Sections
How to identify and graph them.
Classifying Conic Sections
Nonlinear Functions, Conic Sections, and Nonlinear Systems
Conic Sections An Introduction.
Identifying Conic Sections
Conic Sections and Polar Coordinates
Nonlinear Functions, Conic Sections, and Nonlinear Systems
Presentation transcript:

Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Second-Degree Equations in Two Variables Translating Axes versus Translating Graphs Rotation of Axes Discriminant Test … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.

Copyright © 2011 Pearson, Inc. Slide Example Graphing a Second-Degree Equation

Copyright © 2011 Pearson, Inc. Slide Example Graphing a Second-Degree Equation

Copyright © 2011 Pearson, Inc. Slide Example Graphing a Second-Degree Equation

Copyright © 2011 Pearson, Inc. Slide Example Graphing a Second-Degree Equation

Copyright © 2011 Pearson, Inc. Slide Translation-of-Axes Formulas

Copyright © 2011 Pearson, Inc. Slide Example Translation Formula

Copyright © 2011 Pearson, Inc. Slide Example Translation Formula

Copyright © 2011 Pearson, Inc. Slide Example Translation Formula

Copyright © 2011 Pearson, Inc. Slide Rotation-of-Axes Formulas

Copyright © 2011 Pearson, Inc. Slide Rotation of Cartesian Coordinate Axes

Copyright © 2011 Pearson, Inc. Slide Example Rotation of Axes

Copyright © 2011 Pearson, Inc. Slide Example Rotation of Axes

Copyright © 2011 Pearson, Inc. Slide Example Rotation of Axes

Copyright © 2011 Pearson, Inc. Slide Coefficients for a Conic in a Rotated System

Copyright © 2011 Pearson, Inc. Slide Angle of Rotation to Eliminate the Cross-Product Term

Copyright © 2011 Pearson, Inc. Slide Discriminant Test

Copyright © 2011 Pearson, Inc. Slide Conics and the Equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0

Copyright © 2011 Pearson, Inc. Slide Quick Review

Copyright © 2011 Pearson, Inc. Slide Quick Review Solutions

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.