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The Circle

ICSE · Class 11 · Mathematics

Complete topic list for The Circle in ICSE Class 11 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

72 questions28 flashcards5 concepts

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4 Topics · ICSE Class 11 Mathematics

Topics in The Circle

1

1. Basic ideas and terms

  • A circle is the locus of all points in a plane equidistant from a fixed point.
  • The fixed point is called the centre of the circle.
  • The distance from the centre to any point on the circle is called the radius.
2

2. Standard equation of a circle

  • The standard equation of a circle with centre (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.
  • If the centre is at the origin, the equation becomes x^2 + y^2 = r^2.
  • This equation comes directly from the distance formula.
3

3. General equation of a circle

  • The general equation of a circle is x^2 + y^2 + 2gx + 2fy + c = 0.
  • Its centre is (-g,-f).
  • Its radius is sqrt(g^2 + f^2 - c).
4

4. Diameter equation of a circle

  • If the endpoints of a diameter are known, the circle can be found using the diameter equation.
  • The equation is (x-x1)(x-x2) + (y-y1)(y-y2) = 0.
  • This comes from the fact that the angle in a semicircle is a right angle.

Key Concepts

Central concept: Circle as the locus of points in a plane equidistant from a fixed point

Definition of CircleBasic TermsStandard EquationGeneral EquationDiameter EquationParametric EquationPosition of a Point and a CircleRelative Position of Two Circles

Frequently Asked Questions

What are the important topics in The Circle for ICSE Class 11 Mathematics?
Key topics in The Circle include Circle Equations and Properties Overview, Circle Concepts Overview, Circle Equations Overview. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in The Circle — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 72 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.

More resources for The Circle

All 18 chapters — ICSE Class 11 Mathematics Syllabus

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