Unit 1: Locus — Online MCQ Test
MATHEMATICS - 1B · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board
Practice Unit 1: Locus with a free chapter-wise online MCQ test.
This chapter covers: This chapter introduces the definition of locus finding equations of loci under given geometrical conditions and geometric constraints on points..
AI-generated questions from basic to board-exam level, with instant results and explanations.
Unit 1: Locus — Important Questions & Answers
What is the locus of a point in a plane?
- A. A curve or set of points satisfying a given condition
- B. Only a straight line
- C. Only a circle
- D. Any random set of points
Answer: A. A curve or set of points satisfying a given condition
A locus is the path or set of all points that satisfy a specified geometric condition.
A locus is the path or set of all points that satisfy a specified geometric condition.
Which of the following is the locus of points equidistant from two fixed points?
- A. The line joining the two points
- B. The perpendicular bisector of the segment joining the two points
- C. The angle bisector of the angle formed by the points
- D. A circle with the two points as ends of a diameter
Answer: B. The perpendicular bisector of the segment joining the two points
The perpendicular bisector consists of all points equidistant from the two fixed points.
The perpendicular bisector consists of all points equidistant from the two fixed points.
A point moves such that its distance from the x-axis is 3 units. What is the locus?
- A. x = 3 or x = -3
- B. y = 3 or y = -3
- C. x^2 + y^2 = 9
- D. y = x
Answer: B. y = 3 or y = -3
Distance from the x-axis is measured by the absolute value of the y-coordinate, so |y| = 3.
Distance from the x-axis is measured by the absolute value of the y-coordinate, so |y| = 3.
If a point P(x, y) is such that x + y = 5, what is the geometric interpretation of this locus?
- A. A circle with center at origin
- B. A straight line
- C. A parabola
- D. A point
Answer: B. A straight line
An equation of the form ax + by + c = 0 represents a straight line in the plane.
An equation of the form ax + by + c = 0 represents a straight line in the plane.
If a point P(x, y) satisfies the condition that its distance from the origin is equal to the square of its distance from the x-axis, then which equation represents the locus?
- A. x^2 + y^2 = y^4
- B. x^2 + y^2 = y^2
- C. x^2 + y^2 = |y|
- D. x^2 + y^2 = 2y^2
Answer: A. x^2 + y^2 = y^4
Distance from origin is √(x^2+y^2) and distance from x-axis is |y|. Squaring the given relation gives x^2 + y^2 = y^4.
Distance from origin is √(x^2+y^2) and distance from x-axis is |y|. Squaring the given relation gives x^2 + y^2 = y^4.