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Formula Sheet

The Circle

ICSE · Class 11 · Mathematics

All formulas from The Circle in ICSE Class 11 Mathematics. Key equations, constants, and identities for board exam preparation.

72 questions28 flashcards5 concepts

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A labeled diagram illustrating the definition of a circle with its center and radius.
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15 Formulas · 4 Sections

Formulas

1. Core Definitions and Terms

Circle = locus of all points in a plane equidistant from a fixed point

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

Equation of circle centred at origin: x^2+y^2=r^2

General Equation of a Circle: x^2+y^2+2gx+2fy+c=0

Diameter Equation of a Circle: (x-x1)(x-x2)+(y-y1)(y-y2)=0

2. Standard Form and Quick Conversions

If centre is (0,2) and radius is 2, then x^2+(y-2)^2=4

If centre is (-2,3) and radius is 4, then (x+2)^2+(y-3)^2=16

If centre is (0,0) and radius is a, then x^2+y^2=a^2

If centre is (-a,-b) and radius is sqrt(a^2-b^2), then x^2+y^2+2ax+2by+2b^2=0

3. General Equation of a Circle

x^2+y^2+2gx+2fy+c=0

Centre of x^2+y^2-6x+4y-12=0 is (3,-2)

Radius of x^2+y^2-6x+4y-12=0 is 5

For 2x^2+2y^2+3x+4y+9/8=0, divide by 2 first

4. Diameter Equation

(x-x1)(x-x2)+(y-y1)(y-y2)=0

If diameter endpoints are (1,3) and (4,5), equation is (x-1)(x-4)+(y-3)(y-5)=0

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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 Formula Sheet

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