Difference between revisions of "Conic sections"
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− | [http:// | + | [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:// | + | |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] |
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− | [http:// | + | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] |
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− | [http:// | + | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] |
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− | + | '''Concept Map ''' | |
__FORCETOC__ | __FORCETOC__ | ||
+ | [[File:conic_sections.mm|flash]] | ||
+ | |||
= Textbook = | = Textbook = | ||
To add textbook links, please follow these instructions to: | To add textbook links, please follow these instructions to: | ||
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= Teaching Outlines = | = Teaching Outlines = | ||
+ | This page describes the various two dimensional conic sections that can be obtained.[http://en.wikipedia.org/wiki/Conic_section] | ||
+ | ==Concept #1 Conic sections== | ||
+ | ===Learning objectives=== | ||
+ | # 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. | ||
+ | # These figures can be represented on the graph as well as algebraically. | ||
+ | # The four conic sections are circles, ellipses, parabolas, and hyperbolas. | ||
− | |||
− | |||
===Notes for teachers=== | ===Notes for teachers=== | ||
+ | # The general equation for all conics is <math>Ax^2+Bxy+Cy^2+Dx+Ey+F=0</math> | ||
+ | # If <math>B^2-4AC<0</math> then the curve is an ellipse, circle, point or no curve.<br> | ||
+ | # If <math>B^2-4AC=0</math> then the curve is a parabola,2parallel lines, 1 line or no curve.<br> | ||
+ | # If <math>B^2-4AC>0</math> then the curve is a hyperbola or 2 intersecting lines.<br> | ||
+ | |||
===Activity No # === | ===Activity No # === | ||
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− | ''[http:// | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
|} | |} | ||
− | *Estimated Time | + | *Estimated Time: 40 minutes |
*Materials/ Resources needed | *Materials/ Resources needed | ||
*Prerequisites/Instructions, if any | *Prerequisites/Instructions, if any | ||
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{| style="height:10px; float:right; align:center;" | {| style="height:10px; float:right; align:center;" | ||
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− | ''[http:// | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
|} | |} | ||
*Estimated Time | *Estimated Time | ||
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*Question Corner | *Question Corner | ||
− | ==Concept #== | + | ==Concept #2 Hyperbola== |
===Learning objectives=== | ===Learning objectives=== | ||
+ | #Introduction to the form of a hyperbola | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
===Activity No # === | ===Activity No # === | ||
{| style="height:10px; float:right; align:center;" | {| style="height:10px; float:right; align:center;" | ||
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− | ''[http:// | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
+ | |} | ||
+ | *Estimated Time | ||
+ | *Materials/ Resources needed | ||
+ | *Prerequisites/Instructions, if any | ||
+ | *Multimedia resources | ||
+ | *Website interactives/ links/ / Geogebra Applets | ||
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+ | |||
+ | *Process/ Developmental Questions | ||
+ | *Evaluation | ||
+ | *Question Corner | ||
+ | ===Activity No # === | ||
+ | {| 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;"> | ||
+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
|} | |} | ||
*Estimated Time | *Estimated Time | ||
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*Question Corner | *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 # === | ||
+ | {| 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;"> | ||
+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
+ | |} | ||
+ | *Estimated Time | ||
+ | *Materials/ Resources needed | ||
+ | *Prerequisites/Instructions, if any | ||
===Activity No # === | ===Activity No # === | ||
{| 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:// | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
|} | |} | ||
*Estimated Time | *Estimated Time | ||
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*Question Corner | *Question Corner | ||
+ | ==Concept #4 ELLIPSE== | ||
+ | ===Learning objectives=== | ||
+ | #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 # === | ||
+ | {| 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;"> | ||
+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
+ | |} | ||
+ | *Estimated Time | ||
+ | *Materials/ Resources needed | ||
+ | *Prerequisites/Instructions, if any | ||
+ | *Multimedia resources | ||
+ | *Website interactives/ links/ / Geogebra Applets | ||
+ | *Process/ Developmental Questions | ||
+ | *Evaluation | ||
+ | *Question Corner | ||
+ | ===Activity No # === | ||
+ | {| 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;"> | ||
+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
+ | |} | ||
+ | *Estimated Time | ||
+ | *Materials/ Resources needed | ||
+ | *Prerequisites/Instructions, if any | ||
+ | *Multimedia resources | ||
+ | *Website interactives/ links/ / Geogebra Applets | ||
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+ | *Evaluation | ||
+ | *Question Corner | ||
= Hints for difficult problems = | = Hints for difficult problems = | ||
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+ | |||
+ | [[Category:Circles]] |
Latest revision as of 06:09, 21 January 2020
Philosophy of Mathematics |
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This page describes the various two dimensional conic sections that can be obtained.[1]
Concept #1 Conic sections
Learning objectives
- 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.
- These figures can be represented on the graph as well as algebraically.
- The four conic sections are circles, ellipses, parabolas, and hyperbolas.
Notes for teachers
- The general equation for all conics is
- If then the curve is an ellipse, circle, point or no curve.
- If then the curve is a parabola,2parallel lines, 1 line or no curve.
- If then the curve is a hyperbola or 2 intersecting lines.
Activity No #
- Estimated Time: 40 minutes
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Concept #2 Hyperbola
Learning objectives
- Introduction to the form of a hyperbola
Notes for teachers
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- Website interactives/ links/ / Geogebra Applets
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Concept #3. PARABOLA
Learning objectives
Notes for teachers
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Concept #4 ELLIPSE
Learning objectives
- Introduction to the form of a hyperbola
Notes for teachers
- Activity No #
- Click to Comment
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Activity No #
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Activity No #
- Estimated Time
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- Evaluation
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Hints for difficult problems
Project Ideas
Math Fun
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