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Revision Notes

Circles

Telangana Board · Class 12 · Mathematics

Quick revision notes for Circles — Telangana Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

44 questions20 flashcards5 concepts

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Key Topics to Revise

1

Basic Definition and Standard Equation of Circle

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

Finding Circle Equations from Given Conditions

  • Circle through three non-collinear points: substitute coordinates and solve system of equations
  • Circle with given center and passing through a point: use distance formula for radius
  • Circle touching axes: special cases with center coordinates related to radius
3

Position of Point and Power of Point

  • Point P(x₁,y₁) relative to circle S = x² + y² + 2gx + 2fy + c = 0
  • S₁₁ < 0: point inside circle; S₁₁ = 0: point on circle; S₁₁ > 0: point outside circle
  • Power of point = S₁₁ = distance² from center - radius²
4

Tangent and Normal to Circle

  • Equation of tangent at point (x₁,y₁) on circle S = 0 is S₁ = 0
  • For circle x² + y² = r²: tangent at (x₁,y₁) is xx₁ + yy₁ = r²
  • Normal passes through center and point of contact

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Full Notes

Key Concepts

A circle is the locusx² + y² + 2gx +Circle with centre (hFor circle S = x² +Tangent at point (x₁

Frequently Asked Questions

What are the important topics in Circles for Telangana Board Class 12 Mathematics?
Circles covers several key topics that are frequently asked in Telangana Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Circles — Telangana Board Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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