Difference between revisions of "Conic sections"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
m (added Category:Circles using HotCat)
 
(6 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
'''Concept Map '''
+
 
−
__FORCETOC__
 
−
<mm>[[conic_sections.mm|flash]]</mm>
 
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
Line 7: Line 5:
 
|-
 
|-
 
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
+
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
−
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
+
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
|}
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
  
 +
'''Concept Map '''
 +
__FORCETOC__
 +
[[File:conic_sections.mm|flash]]
  
 
= Textbook =
 
= Textbook =
Line 35: Line 36:
 
==Concept #1 Conic sections==
 
==Concept #1 Conic sections==
 
===Learning objectives===
 
===Learning objectives===
−
[[File:conic  sections.gif|200px|right]]
 
 
# Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane.  
 
# Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane.  
 
# There are different ways to do this, and each way yields a different figure.  
 
# There are different ways to do this, and each way yields a different figure.  
 
# These figures can be represented on the graph as well as algebraically.  
 
# These figures can be represented on the graph as well as algebraically.  
 
# The four conic sections are circles, ellipses, parabolas, and hyperbolas.
 
# The four conic sections are circles, ellipses, parabolas, and hyperbolas.
−
 
 
−
 
  
 
===Notes for teachers===
 
===Notes for teachers===
Line 52: Line 50:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time: 40 minutes
 
*Estimated Time: 40 minutes
Line 66: Line 64:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 84: Line 82:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 99: Line 97:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 123: Line 121:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 131: Line 129:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 173: Line 171:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 186: Line 184:
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
−
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
|}
 
*Estimated Time
 
*Estimated Time
Line 206: Line 204:
  
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 +
 +
[[Category:Circles]]

Latest revision as of 06:09, 21 January 2020

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]

Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

Useful websites

Reference Books

Teaching Outlines

This page describes the various two dimensional conic sections that can be obtained.[1]

Concept #1 Conic sections

Learning objectives

  1. Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane.
  2. There are different ways to do this, and each way yields a different figure.
  3. These figures can be represented on the graph as well as algebraically.
  4. The four conic sections are circles, ellipses, parabolas, and hyperbolas.

Notes for teachers

  1. The general equation for all conics is
  2. If then the curve is an ellipse, circle, point or no curve.
  3. If then the curve is a parabola,2parallel lines, 1 line or no curve.
  4. If then the curve is a hyperbola or 2 intersecting lines.

Activity No #

  • Estimated Time: 40 minutes
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #2 Hyperbola

Learning objectives

  1. Introduction to the form of a hyperbola

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets

  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner


  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #3. PARABOLA

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #4 ELLIPSE

Learning objectives

  1. Introduction to the form of a hyperbola

Notes for teachers

  • Activity No #
  • Click to Comment
  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner
  • Activity No #
  • Click to Comment
  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Hints for difficult problems

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template

Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Conic_sections&oldid=33237"