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Revision Notes

Locus

ICSE · Class 10 · Mathematics

Quick revision notes for Locus — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

37 questions24 flashcards5 concepts

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An illustration defining locus as the path of a moving point under a given condition, with a specific example of a point at a fixed distance from a fixed point forming a circle.
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Key Topics to Revise

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1. Core Idea of Locus

  • The locus of a moving point is the path traced under the given condition.
  • Every point which satisfies the given conditions lies on the locus.
  • Every point which lies on the locus, satisfies the given condition(s).
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2. Theorem 1: Points Equidistant from Two Fixed Points

  • The locus of a point equidistant from two given points is the perpendicular bisector of the line segment joining the two points.
  • This theorem is tested separately from the theorem about intersecting lines.
  • If P satisfies PA = PB, then P lies on the perpendicular bisector of AB.
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3. Theorem 2: Points Equidistant from Two Intersecting Lines

  • The locus of a point equidistant from two intersecting lines is the pair of lines bisecting the angles between the lines.
  • The pair of lines is X'OX and Y'OY, not a single line.
  • If P is equidistant from the two lines, then P lies on one of the angle bisectors.
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4. Standard Locus Cases

  • The locus of a point which is equidistant from two parallel straight lines is a straight line parallel to the given lines and mid-way between them.
  • The locus of a point which is at a given distance from a given straight line consists of a pair of straight lines parallel to the given line and at a given distance from it.
  • The locus of the centre of a wheel, which moves on a straight horizontal road, is a straight line parallel to the road and at a distance equal to the radius of the wheel.

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Full Notes

Key Concepts

The locus of a moving pointA point at a fixed distanceThe locus of a point equidistantThe locus of a point equidistantThe locus of a point at

Frequently Asked Questions

What are the important topics in Locus for ICSE Class 10 Mathematics?
Locus covers several key topics that are frequently asked in ICSE Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Locus — ICSE Class 10 Mathematics?
Understand the core concepts first, then work through the 37 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.

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