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Study Plan

Circles — Study Plan

Telangana Open School (TOSS) · Class 12 · Mathematics

A step-by-step study plan for Circles, Telangana Open School (TOSS) Class 12 Mathematics: what to learn first, what to practise and when to revise.

48 questions25 flashcards14 formulas & key relations5 concepts

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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: Standard and General Equation of a Circle, Special Cases and Diameter Form, Tangents, Normals, and Chords.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 48 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Circles after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • A circle is the set of points equidistant from a center.
  • Standard form: $(x - h)^2 + (y - k)^2 = r^2$
  • Center: (h, k), Radius: r
  • General form: $x^2 + y^2 + 2gx + 2fy + c = 0$
  • Center: $(-g, -f)$
  • Radius: $\sqrt{g^2 + f^2 - c}$
  • Three non-collinear points determine a unique circle.
  • Substitute points into general equation and solve for g, f, c.

Common Mistakes to Avoid

The general equation of a circle is always in the form x² + y² + 2gx + 2fy + c = 0, so any second-degree equation must represent a circle.

If a circle touches the x-axis, then k = r, so the equation becomes (x - h)² + (y - r)² = r².

The diameter form of a circle is (x - x₁)² + (y - y₁)² = (x₂ - x₁)² + (y₂ - y₁)².

Memory Tips

Standard Equation of a Circle: (x - h)² + (y - k)² = r²

General Form: x² + y² + 2gx + 2fy + c = 0

Center is (−g, −f) in general form

Radius = √(g² + f² − c)

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Frequently Asked Questions

What are the important topics in Circles for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Circles include Standard and General Equation of a Circle, Special Cases and Diameter Form, Tangents, Normals, and Chords, Relative Position of Two Circles and Orthogonality. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Circles for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 48 practice questions on Circles. 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 Circles

All Telangana Open School (TOSS) Class 12 Mathematics Study Plan

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