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Revision Notes

Locus — Revision Notes

ICSE · Class 10 · Mathematics

Locus revision notes for ICSE Class 10 Mathematics: 4 topics in quick points. Part of the ICSE Class 10 Mathematics syllabus.

37 questions24 flashcards5 formulas & key relations5 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

1

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).
2

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.
3

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.
4

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?
Key topics in Locus include Core Idea of Locus, Theorem 1: Points Equidistant from Two Fixed Points, Theorem 2: Points Equidistant from Two Intersecting Lines, Standard Locus Cases. Study these first, then practise questions on each for the ICSE Class 10 board exam.
How should I revise Locus for the ICSE Class 10 board exam?
Learn the core ideas first, then work through the 37 practice questions on Locus. 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 10 Mathematics Revision Notes

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