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Two Dimensional Analytical Geometry-II

Tamil Nadu Board · Class 12 · Mathematics

Complete topic list for Two Dimensional Analytical Geometry-II in Tamil Nadu Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions30 flashcards5 concepts

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4 Topics · Tamil Nadu Board Class 12 Mathematics

Topics in Two Dimensional Analytical Geometry-II

1

5.2 Circle - Equations and Properties

  • A circle is the locus of points equidistant from a fixed point (centre)
  • Standard form: (x - h)² + (y - k)² = r² where centre is (h,k) and radius is r
  • General form: x² + y² + 2gx + 2fy + c = 0 where centre is (-g,-f) and radius is √(g² + f² - c)
2

5.3 Conics - Definition and Classification

  • A conic is locus of point P such that its distance from fixed point (focus) divided by distance from fixed line (directrix) equals constant (eccentricity e)
  • If e = 1: parabola; if 0 < e < 1: ellipse; if e > 1: hyperbola
  • General equation: Ax² + Bxy + Cy² + Dx + Ey + F = 0
3

5.3.2 Parabola - Equation and Properties

  • Standard form: y² = 4ax (opens right); y² = -4ax (opens left); x² = 4ay (opens up); x² = -4ay (opens down)
  • For y² = 4ax: vertex (0,0), focus (a,0), directrix x = -a, axis = x-axis, latus rectum length = 4a
  • Vertex form with vertex at (h,k): (y-k)² = 4a(x-h) or (x-h)² = 4a(y-k)
4

5.3.3 Ellipse - Equation and Properties

  • Standard form: x²/a² + y²/b² = 1 where a > b (major axis along x); or x²/b² + y²/a² = 1 where a > b (major axis along y)
  • For major axis along x: centre (0,0), vertices (±a,0), foci (±c,0) where c² = a² - b², eccentricity e = c/a < 1
  • Sum of focal distances constant: SP + S'P = 2a for any point P on ellipse

Key Concepts

A circle is the locusA conic is the locusA parabola (e=1) is the locusAn ellipse (0<e<1) has the propertyA hyperbola (e>1) has the property

Frequently 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 Two Dimensional Analytical Geometry-II Concept Map, Complete Mind Map of Two Dimensional Analytical Geometry-II, Two Dimensional Analytical Geometry-II: Complete Concept Map. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Two Dimensional Analytical Geometry-II — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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.

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