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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-20-LP-01
Locus at a Fixed Distance from a Point — Assignment
Chapter: Loci
Topic: Locus of a Point at a Fixed Distance from a Point
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The locus of points at a fixed distance from a fixed point is a:
  • A.line
  • B.circle
  • C.pair of lines
  • D.parabola
2.
The fixed point is the:
  • A.radius
  • B.centre
  • C.diameter
  • D.chord
3.
The fixed distance is the:
  • A.centre
  • B.radius
  • C.arc
  • D.chord
4.
Points $5$ cm from $O$ form a circle of radius:
  • A.$2.5$ cm
  • B.$5$ cm
  • C.$10$ cm
  • D.$25$ cm
5.
A locus is a set of points satisfying a given:
  • A.number
  • B.condition
  • C.graph
  • D.ratio
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Name the locus of points $3$ cm from a point $O$.
7.
What is the centre of such a locus?
8.
What is the radius if the points are $7$ cm from $O$?
9.
In a plane, is this locus a circle or a sphere?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Describe the locus of a point that is always $4$ cm from a fixed point $A$.
11.
Describe the locus of points $6$ cm from one of two points $6$ cm apart.
12.
What is the locus traced by the tip of a clock hand?
13.
State the locus of points at distance $r$ from a point $O$ in three dimensions.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Describe the locus of a point $P$ whose distance from a fixed point $O$ is always $5$ cm, and state how many such points lie on a given line through $O$.
15.
A point moves so that it is always $4$ cm from a fixed point. If it also lies on a straight line $3$ cm from that point, how many positions are possible?

Answer Key

Section A — Multiple Choice Questions
  1. (B) circle
  2. (B) centre
  3. (B) radius
  4. (B) $5$ cm
  5. (B) condition
Section B — Short Answer (2 marks)
  1. A circle of radius $3$ cm centred at $O$.
  2. The fixed point.
  3. $7$ cm.
  4. A circle.
Section C — Short Answer (3 marks)
  1. A circle of radius $4$ cm, centre $A$.
  2. A circle of radius $6$ cm around that point.
  3. A circle.
  4. A sphere of radius $r$.
Section D — Long Answer (5 marks)
  1. A circle of radius $5$ cm centred at $O$; a line through $O$ meets it at $2$ points.
  2. $2$ positions (the line is a secant since $3<4$).
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