Chapter 9 of 12
Concept Maps
Two Dimensional Analytical Geometry-II — Concept Maps
Tamil Nadu Board · Class 12 · Mathematics
3 concept maps of Two Dimensional Analytical Geometry-II for Tamil Nadu Board Class 12 Mathematics, each also written out as a text outline.
45 questions30 flashcards12 formulas & key relations5 concepts
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3 Concept Maps
Two Dimensional Analytical Geometry-II Concept Map
The map in words
- Two Dimensional Analytical Geometry-II
- Circles
- Standard Form
- General Form
- Tangent and Normal
- Position of Points
- Parabola
- Standard Forms
- Vertex and Focus
- Latus Rectum
- Tangent Conditions
- Ellipse
- Standard Forms
- Major and Minor Axes
- Eccentricity
- Focal Properties
- Latus Rectum
- Hyperbola
- Standard Forms
- Transverse Axis
- Eccentricity
- Asymptotes
- Focal Properties
- Tangents and Normals
- Cartesian Form
- Parametric Form
- Conditions for Tangency
- Applications
- Parabolic Mirrors
- Elliptical Orbits
- Hyperbolic Navigation
- Architectural Designs
- Circles
Complete Mind Map of Two Dimensional Analytical Geometry-II
The map in words
- Analytical Geometry II
- Circles
- Standard Form
- (x-h)² + (y-k)² = r²
- Centre and radius
- General Form
- x² + y² + 2gx + 2fy + c = 0
- -g,-f
- Radius √(g²+f²-c)
- Tangent and Normal
- Tangent: xx₁ + yy₁ + g(x+x₁) + f(y+y₁) + c = 0
- Normal passes through centre
- Position of Point
- S > 0 Outside
- S = 0 On circle
- S < 0 Inside
- Standard Form
- Conics
- e=1
- Standard forms
- y²=4ax, x²=4ay
- Vertex, focus, directrix
- Parametric: x=at², y=2at
- Tangent and normal
- 0<e<1
- Standard forms
- x²/a² + y²/b² = 1
- Foci at (±c,0)
- e = c/a
- Sum of focal distances = 2a
- Parametric: x=acosθ, y=bsinθ
- e>1
- Standard forms
- x²/a² - y²/b² = 1
- Foci, vertices, asymptotes
- c² = a² + b²
- Difference of focal distances = 2a
- Parametric: x=asecθ, y=btanθ
- Tangents and Normals
- Cartesian form at point
- Parametric form
- Condition for line y=mx+c
- Director circles
- e=1
- Applications
- Parabola
- Headlights, flashlights
- Satellite dishes
- Solar cookers
- Arches and bridges
- Ellipse
- Planetary orbits
- Whispering galleries
- Lithotripter device
- Earth shape
- Hyperbola
- Comets
- Cooling towers
- Ship location systems
- Telescope design
- Parabola
- Circles
Two Dimensional Analytical Geometry-II: Complete Concept Map
The map in words
- Conic Sections
- Circle
- Standard Form
- Center h,k
- Radius r
- General Form
- 2gx 2fy c
- Center -g,-f
- Equation of Tangent
- Equation of Normal
- Standard Form
- Parabola
- Eccentricity e=1
- Standard Forms
- y²=4ax opens right
- x²=4ay opens up
- Focus and Directrix
- Latus Rectum 4a
- Reflective Property
- Ellipse
- Eccentricity 0<e<1
- Sum of Focal Distances
- Always equals 2a
- Standard Form
- x²/a² y²/b²=1
- Major and Minor Axes
- Foci and Vertices
- Latus Rectum 2b²/a
- Hyperbola
- Eccentricity e>1
- Difference of Focal Distances
- Always equals 2a
- Standard Form
- x²/a² - y²/b²=1
- Asymptotes b/a slope
- Transverse and Conjugate Axes
- Tangents and Normals
- Cartesian Form
- Parametric Form
- Condition for Tangency
- Point of Contact
- Parametric Equations
- Circle
- x=a cos θ
- y=a sin θ
- Parabola
- x=at²
- y=2at
- Ellipse
- x=a cos θ
- y=b sin θ
- Hyperbola
- x=a sec θ
- y=b tan θ
- Circle
- Identifying Conics
- General Equation
- Discriminant B²-4AC
- Circle A=C B=0
- Parabola B=0
- Ellipse Same Signs
- Hyperbola Opposite Signs
- Real-world Applications
- Engineering
- Bridges
- Towers
- Antennas
- Astronomy
- Planetary Orbits
- Comet Paths
- Medical
- Lithotripter
- Imaging
- Architecture
- Domes
- Arches
- Engineering
- Circle
Explore these maps interactively
Explore DiagramsFrequently Asked Questions
What are the important topics in Two Dimensional Analytical Geometry-II for Tamil Nadu Board Class 12 Mathematics?
Key topics in Two Dimensional Analytical Geometry-II include 2 Circle - Equations and Properties, 3 Conics - Definition and Classification, 3.2 Parabola - Equation and Properties, 3.3 Ellipse - Equation and Properties. Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
What do the concept maps for Two Dimensional Analytical Geometry-II show?
The 3 maps show how the ideas in Two Dimensional Analytical Geometry-II connect: Two Dimensional Analytical Geometry-II Concept Map; Complete Mind Map of Two Dimensional Analytical Geometry-II. Each map is also written out as an outline on this page.
How should I revise Two Dimensional Analytical Geometry-II for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Two Dimensional Analytical Geometry-II. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Two Dimensional Analytical Geometry-II
Practice Quiz
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Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
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