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Important Questions

The Circle

ICSE · Class 11 · Mathematics

Most important questions from The Circle for ICSE Class 11 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

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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72 Questions·
multiple choicemultiple correct

Sample Questions

1multiple choice
3 marks

A circle has centre (0, 0) and passes through the points (3, 4) and (-4, 3). What is its equation?

Show answer

x^2 + y^2 = 25

Since the centre is (0, 0), the radius is the distance to (3, 4): sqrt(3^2 + 4^2) = 5. The same result is obtained from (-4, 3). Therefore the equation is x^2 + y^2 = 25.

2multiple choice
3 marks

A point P(x, y) is given by x = 2 + 3 cos θ and y = 3 sin θ, where 0 ≤ θ < 2π. What Cartesian equation does P satisfy?

Show answer

(x - 2)^2 + y^2 = 9

From x = 2 + 3 cos θ, we get (x - 2)/3 = cos θ. From y = 3 sin θ, we get y/3 = sin θ. Squaring and adding gives (x - 2)^2/9 + y^2/9 = 1, so (x - 2)^2 + y^2 = 9.

3multiple choice
3 marks

A point P(x, y) is given by x = -2 + 5 cos θ and y = 4 + 3 sin θ, where 0 ≤ θ < 2π. Which equation represents the locus of P?

Show answer

9(x + 2)^2 + 25(y - 4)^2 = 225

Rewrite as (x + 2)/5 = cos θ and (y - 4)/3 = sin θ. Squaring and adding gives (x + 2)^2/25 + (y - 4)^2/9 = 1, or 9(x + 2)^2 + 25(y - 4)^2 = 225. Since the coefficients of x^2 and y^2 are different, it is not a circle.

4multiple choice
3 marks

A circle has diameter endpoints (1, 3) and (4, 5). What is its equation?

Show answer

(x - 1)(x - 4) + (y - 3)(y - 5) = 0

Using the diameter equation with endpoints (x1, y1) = (1, 3) and (x2, y2) = (4, 5), the equation is (x - x1)(x - x2) + (y - y1)(y - y2) = 0. Substituting gives (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.
How many important questions are there in The Circle?
There are 72 practice questions available for The Circle. These cover multiple question types including MCQs, short answer, and long answer questions.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 18 chapters — ICSE Class 11 Mathematics Important Questions

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