SlideShare a Scribd company logo
1 of 8
Rotation of Axes
Identification of a Conic
                    Prepared by:
        Prof. Teresita P. Liwanag – Zapanta
 B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)
SPECIFIC OBJECTIVES:
       At the end of the lesson, the student is expected to be
able to:

• transform an equation by rotation of axes.
• simplify the equations by rotation of axes.
• identify a conic given an equation.
• graph the transformed equation.
Lesson 12    rotation of axes
Lesson 12    rotation of axes
Lesson 12    rotation of axes
Lesson 12    rotation of axes
Lesson 12    rotation of axes
Lesson 12    rotation of axes

More Related Content

What's hot

Lesson 14 b - parametric-1
Lesson 14 b - parametric-1Lesson 14 b - parametric-1
Lesson 14 b - parametric-1Jean Leano
 
Lesson 15 polar curves
Lesson 15    polar curvesLesson 15    polar curves
Lesson 15 polar curvesJean Leano
 
spherical coordinates system
spherical coordinates systemspherical coordinates system
spherical coordinates systemPankaj Nakum
 
Analytic geometry lecture1
Analytic geometry lecture1Analytic geometry lecture1
Analytic geometry lecture1admercano101
 
Hyperbola (Introduction)
Hyperbola (Introduction)Hyperbola (Introduction)
Hyperbola (Introduction)rey castro
 
Writing Equations of a Line
Writing Equations of a LineWriting Equations of a Line
Writing Equations of a Lineswartzje
 
Slope Powerpoint
Slope PowerpointSlope Powerpoint
Slope Powerpointguesta9ee9b
 
linear transformation
linear transformationlinear transformation
linear transformationmansi acharya
 
Conic sections circles - STEM TEACH
Conic sections circles - STEM TEACHConic sections circles - STEM TEACH
Conic sections circles - STEM TEACHMr Math
 
Solving Systems of Linear Inequalities
Solving Systems of Linear InequalitiesSolving Systems of Linear Inequalities
Solving Systems of Linear Inequalitiesswartzje
 
Lesson 8 conic sections - parabola
Lesson 8    conic sections - parabolaLesson 8    conic sections - parabola
Lesson 8 conic sections - parabolaJean Leano
 
Conic section- Hyperbola STEM TEACH
Conic section- Hyperbola STEM TEACHConic section- Hyperbola STEM TEACH
Conic section- Hyperbola STEM TEACHMr Math
 
The remainder theorem powerpoint
The remainder theorem powerpointThe remainder theorem powerpoint
The remainder theorem powerpointJuwileene Soriano
 
Householder transformation | Householder Reflection with QR Decomposition
Householder transformation | Householder Reflection with QR DecompositionHouseholder transformation | Householder Reflection with QR Decomposition
Householder transformation | Householder Reflection with QR DecompositionIsaac Yowetu
 
Cylindrical co ordinate system
Cylindrical co ordinate systemCylindrical co ordinate system
Cylindrical co ordinate systemNisarg Amin
 

What's hot (20)

Lesson 14 b - parametric-1
Lesson 14 b - parametric-1Lesson 14 b - parametric-1
Lesson 14 b - parametric-1
 
Lesson 15 polar curves
Lesson 15    polar curvesLesson 15    polar curves
Lesson 15 polar curves
 
spherical coordinates system
spherical coordinates systemspherical coordinates system
spherical coordinates system
 
Hyperbola
HyperbolaHyperbola
Hyperbola
 
R lecture co2_math 21-1
R lecture co2_math 21-1R lecture co2_math 21-1
R lecture co2_math 21-1
 
Analytic geometry lecture1
Analytic geometry lecture1Analytic geometry lecture1
Analytic geometry lecture1
 
Hyperbola (Introduction)
Hyperbola (Introduction)Hyperbola (Introduction)
Hyperbola (Introduction)
 
Ellipse (h,k)
Ellipse (h,k)Ellipse (h,k)
Ellipse (h,k)
 
Writing Equations of a Line
Writing Equations of a LineWriting Equations of a Line
Writing Equations of a Line
 
Slope Powerpoint
Slope PowerpointSlope Powerpoint
Slope Powerpoint
 
linear transformation
linear transformationlinear transformation
linear transformation
 
Conic sections circles - STEM TEACH
Conic sections circles - STEM TEACHConic sections circles - STEM TEACH
Conic sections circles - STEM TEACH
 
Solving Systems of Linear Inequalities
Solving Systems of Linear InequalitiesSolving Systems of Linear Inequalities
Solving Systems of Linear Inequalities
 
Lesson 8 conic sections - parabola
Lesson 8    conic sections - parabolaLesson 8    conic sections - parabola
Lesson 8 conic sections - parabola
 
Conic section- Hyperbola STEM TEACH
Conic section- Hyperbola STEM TEACHConic section- Hyperbola STEM TEACH
Conic section- Hyperbola STEM TEACH
 
The remainder theorem powerpoint
The remainder theorem powerpointThe remainder theorem powerpoint
The remainder theorem powerpoint
 
Householder transformation | Householder Reflection with QR Decomposition
Householder transformation | Householder Reflection with QR DecompositionHouseholder transformation | Householder Reflection with QR Decomposition
Householder transformation | Householder Reflection with QR Decomposition
 
Trapezoidal rule
Trapezoidal rule Trapezoidal rule
Trapezoidal rule
 
Cylindrical co ordinate system
Cylindrical co ordinate systemCylindrical co ordinate system
Cylindrical co ordinate system
 
Math14 lesson 5
Math14 lesson 5Math14 lesson 5
Math14 lesson 5
 

More from Jean Leano

Lesson 14 a - parametric equations
Lesson 14 a - parametric equationsLesson 14 a - parametric equations
Lesson 14 a - parametric equationsJean Leano
 
Lesson 13 algebraic curves
Lesson 13    algebraic curvesLesson 13    algebraic curves
Lesson 13 algebraic curvesJean Leano
 
Lesson 9 conic sections - ellipse
Lesson 9    conic sections - ellipseLesson 9    conic sections - ellipse
Lesson 9 conic sections - ellipseJean Leano
 
Lesson 6 straight line
Lesson 6    straight lineLesson 6    straight line
Lesson 6 straight lineJean Leano
 
Lesson 5 locus of a point
Lesson 5    locus of a pointLesson 5    locus of a point
Lesson 5 locus of a pointJean Leano
 
Lesson 4 division of a line segment
Lesson 4   division of a line segmentLesson 4   division of a line segment
Lesson 4 division of a line segmentJean Leano
 
Lesson 3 angle between two intersecting lines
Lesson 3   angle between two intersecting linesLesson 3   angle between two intersecting lines
Lesson 3 angle between two intersecting linesJean Leano
 
Lesson 2 inclination and slope of a line
Lesson 2   inclination and slope of a lineLesson 2   inclination and slope of a line
Lesson 2 inclination and slope of a lineJean Leano
 
Lesson 1: distance between two points
Lesson 1: distance between two pointsLesson 1: distance between two points
Lesson 1: distance between two pointsJean Leano
 

More from Jean Leano (9)

Lesson 14 a - parametric equations
Lesson 14 a - parametric equationsLesson 14 a - parametric equations
Lesson 14 a - parametric equations
 
Lesson 13 algebraic curves
Lesson 13    algebraic curvesLesson 13    algebraic curves
Lesson 13 algebraic curves
 
Lesson 9 conic sections - ellipse
Lesson 9    conic sections - ellipseLesson 9    conic sections - ellipse
Lesson 9 conic sections - ellipse
 
Lesson 6 straight line
Lesson 6    straight lineLesson 6    straight line
Lesson 6 straight line
 
Lesson 5 locus of a point
Lesson 5    locus of a pointLesson 5    locus of a point
Lesson 5 locus of a point
 
Lesson 4 division of a line segment
Lesson 4   division of a line segmentLesson 4   division of a line segment
Lesson 4 division of a line segment
 
Lesson 3 angle between two intersecting lines
Lesson 3   angle between two intersecting linesLesson 3   angle between two intersecting lines
Lesson 3 angle between two intersecting lines
 
Lesson 2 inclination and slope of a line
Lesson 2   inclination and slope of a lineLesson 2   inclination and slope of a line
Lesson 2 inclination and slope of a line
 
Lesson 1: distance between two points
Lesson 1: distance between two pointsLesson 1: distance between two points
Lesson 1: distance between two points
 

Recently uploaded

Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...ZurliaSoop
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxEsquimalt MFRC
 
SOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning PresentationSOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning Presentationcamerronhm
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...Nguyen Thanh Tu Collection
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and ModificationsMJDuyan
 
Single or Multiple melodic lines structure
Single or Multiple melodic lines structureSingle or Multiple melodic lines structure
Single or Multiple melodic lines structuredhanjurrannsibayan2
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfSherif Taha
 
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...Pooja Bhuva
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfNirmal Dwivedi
 
Graduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - EnglishGraduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - Englishneillewis46
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxDenish Jangid
 
Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)Jisc
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxVishalSingh1417
 
Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)Jisc
 
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdf
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdfUnit 3 Emotional Intelligence and Spiritual Intelligence.pdf
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdfDr Vijay Vishwakarma
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17Celine George
 
Towards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxTowards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxJisc
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxheathfieldcps1
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...pradhanghanshyam7136
 
Interdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptxInterdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptxPooja Bhuva
 

Recently uploaded (20)

Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
 
SOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning PresentationSOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning Presentation
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and Modifications
 
Single or Multiple melodic lines structure
Single or Multiple melodic lines structureSingle or Multiple melodic lines structure
Single or Multiple melodic lines structure
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdf
 
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
Sensory_Experience_and_Emotional_Resonance_in_Gabriel_Okaras_The_Piano_and_Th...
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
 
Graduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - EnglishGraduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - English
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
 
Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)Accessible Digital Futures project (20/03/2024)
Accessible Digital Futures project (20/03/2024)
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
 
Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)Jamworks pilot and AI at Jisc (20/03/2024)
Jamworks pilot and AI at Jisc (20/03/2024)
 
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdf
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdfUnit 3 Emotional Intelligence and Spiritual Intelligence.pdf
Unit 3 Emotional Intelligence and Spiritual Intelligence.pdf
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
 
Towards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxTowards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptx
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
 
Interdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptxInterdisciplinary_Insights_Data_Collection_Methods.pptx
Interdisciplinary_Insights_Data_Collection_Methods.pptx
 

Lesson 12 rotation of axes

  • 1. Rotation of Axes Identification of a Conic Prepared by: Prof. Teresita P. Liwanag – Zapanta B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)
  • 2. SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be able to: • transform an equation by rotation of axes. • simplify the equations by rotation of axes. • identify a conic given an equation. • graph the transformed equation.