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Two Dimensional Analytical Geometry-II — Revision Notes

Tamil Nadu Board · Class 12 · Mathematics

Two Dimensional Analytical Geometry-II revision notes for Tamil Nadu Board Class 12 Mathematics: 4 topics in quick points.

45 questions30 flashcards12 formulas & key relations5 concepts

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Key Topics to Revise

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

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Full Notes

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 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.
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.

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All Tamil Nadu Board Class 12 Mathematics Revision Notes

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