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The Circle — Revision Notes

ICSE · Class 11 · Mathematics

The Circle revision notes for ICSE Class 11 Mathematics: 4 topics in quick points. Part of the ICSE Class 11 Mathematics syllabus.

72 questions28 flashcards20 formulas & key relations5 concepts

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A labeled diagram illustrating the definition of a circle with its center and radius.
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Key Topics to Revise

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.

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Full Notes

Key Concepts

A circle is the locusThe standard equation is (xThe general equation is x^2+y^2+2gx+2fy+c=0If the endA circle with centre (h

Frequently Asked Questions

What are the important topics in The Circle for ICSE Class 11 Mathematics?
Key topics in The Circle include Basic ideas and terms, Standard equation of a circle, General equation of a circle, Diameter equation of a circle. Study these first, then practise questions on each for Class 11 exams.
How should I revise The Circle for Class 11 exams?
Learn the core ideas first, then work through the 72 practice questions on The Circle. 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 ICSE Class 11 Mathematics Revision Notes

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