JEE Main - Locus and its equation Online Test (MCQ Quiz)

1. What is the locus of a point that moves such that its distance from a fixed point is constant?

A) A straight line B) A circle C) A parabola D) An ellipse

2. Find the equation of the locus of a point P(x, y) which is equidistant from points A(2, 3) and B(4, 5).

A) x + y = 10 B) x - y = -2 C) 2x + 2y = 12 D) x + y = 5

3. What is the locus of a point that moves such that its distance from a fixed line is constant?

A) A circle B) Two parallel lines C) A parabola D) A hyperbola

4. If a point P(x, y) moves such that its distance from the x-axis is always 5, what is its locus?

A) y = 5 B) x = 5 C) y = -5 D) y = 5 or y = -5

5. The locus of a point equidistant from two fixed points is:

A) A point B) A line segment C) The perpendicular bisector of the line segment joining the two points D) A circle

6. Find the equation of the locus of a point P(x, y) that moves such that PA = PB, where A = (1, 2) and B = (3, 4).

A) x + y = 6 B) x - y = -2 C) 2x + 2y = 12 D) x + y = 5

7. What is the locus of a point that moves such that its distance from a fixed point (focus) is always equal to its distance from a fixed line (directrix)?

A) Circle B) Ellipse C) Parabola D) Hyperbola

8. The equation of the locus of a point (x, y) that is equidistant from the origin (0, 0) and the point (4, 0) is:

A) x = 2 B) y = 2 C) x = 4 D) y = 0

9. A point P moves such that its distance from point A(1, 0) is always twice its distance from point B(0, 1). Find the locus of P.

A) x^2 + y^2 = 4/3 B) 3x^2 + 3y^2 - 2x - 4y + 1 = 0 C) x^2 - y^2 = 1 D) x + y = 3

10. What is the locus of a point that moves such that the sum of its distances from two fixed points is constant?

A) Circle B) Parabola C) Hyperbola D) Ellipse

11. The locus of a point P(x, y) such that the area of the triangle formed by P and the points (1, 0) and (0, 1) is 1/2 is:

A) x + y = 1 B) x - y = 1 C) x + y = 0 D) x = 1

12. Find the equation of the locus of a point P(x, y) which is at a distance of 5 units from the point (2, 3).

A) (x - 2)^2 + (y - 3)^2 = 25 B) (x + 2)^2 + (y + 3)^2 = 5 C) (x - 2)^2 + (y - 3)^2 = 5 D) (x + 2)^2 + (y + 3)^2 = 25

13. The locus of a point P(x, y) such that the distance from P to the line 3x + 4y - 5 = 0 is 2 is given by:

A) (3x + 4y - 5)^2 = 4(3^2 + 4^2) B) 3x + 4y - 5 = 2 C) 3x + 4y - 5 = -2 D) 3x + 4y - 5 = 10

14. What is the locus of a point that moves such that the difference of its distances from two fixed points is constant?

A) Circle B) Ellipse C) Parabola D) Hyperbola

15. Find the locus of a point P(x, y) which is equidistant from the x-axis and the y-axis.

A) y = x B) y = -x C) y = x or y = -x D) x = 0

16. The equation of the locus of a point P(x, y) that moves such that its distance from A(2, 1) is equal to its distance from the y-axis is:

A) (x - 2)^2 + (y - 1)^2 = x^2 B) (x - 2)^2 + (y - 1)^2 = y^2 C) x^2 + y^2 = x D) x^2 + y^2 = y

17. What is the locus of a point P(x, y) such that OP = 2, where O is the origin?

A) x^2 + y^2 = 4 B) x^2 + y^2 = 2 C) x + y = 2 D) x = 2

18. Find the equation of the locus of a point P(x, y) which moves such that it is always equidistant from the points (a, 0) and (0, b).

A) bx + ay = (a^2 + b^2)/2 B) ax + by = (a^2 + b^2)/2 C) bx - ay = (a^2 - b^2)/2 D) ax - by = (a^2 - b^2)/2

19. The locus of a point P(x, y) such that the sum of the squares of its distances from the points (1, 0) and (-1, 0) is 10, is:

A) x^2 + y^2 = 4 B) x^2 + y^2 = 10 C) x^2 + y^2 = 5 D) x^2 + y^2 = 8

20. What is the locus of a point P(x, y) that moves such that its distance from the point (2, 3) is equal to its distance from the line y = 1?

A) A circle B) A parabola C) An ellipse D) A hyperbola

21. Find the equation of the locus of a point P(x, y) that moves such that its distance from the x-axis is half its distance from the y-axis.

A) y^2 = x^2/4 B) x^2 = y^2/4 C) y = x/2 D) x = y/2

22. The locus of a point P(x, y) such that the product of its distances from the points (a, 0) and (-a, 0) is b^2, is:

A) x^2/a^2 + y^2/b^2 = 1 B) x^2/b^2 + y^2/a^2 = 1 C) (x^2 - a^2)/b^2 + y^2/b^2 = 1 D) x^2/a^2 + y^2/(b^2-a^2) = 1

23. What is the locus of a point P(x, y) such that the distance from P to the origin is equal to the distance from P to the line x = 5?

A) A parabola with vertex at (2.5, 0) B) A parabola with vertex at (0, 2.5) C) A circle with center at (2.5, 0) D) An ellipse with foci at (0, 0) and (5, 0)

24. Find the equation of the locus of a point P(x, y) that moves such that the sum of its distances from A(0, 2) and B(0, -2) is 6.

A) x^2/5 + y^2/9 = 1 B) x^2/9 + y^2/5 = 1 C) x^2/5 + y^2/6 = 1 D) x^2/6 + y^2/5 = 1

25. The locus of a point P(x, y) such that the distance from P to the point (2, 0) is equal to the distance from P to the line x = -2, is:

A) A parabola y^2 = 8x B) A parabola y^2 = -8x C) A parabola x^2 = 8y D) A parabola x^2 = -8y

26. Find the equation of the locus of a point P(x, y) that is equidistant from the point (3, 0) and the y-axis.

A) (x - 3)^2 + y^2 = x^2 B) (x - 3)^2 + y^2 = y^2 C) x^2 + y^2 = 3 D) y^2 = 6x - 9

27. What is the locus of a point P(x, y) such that the sum of the squares of its distances from the axes is 16?

A) x^2 + y^2 = 16 B) x^2 + y^2 = 4 C) x^2 + y^2 = 8 D) x^2 + y^2 = 32

28. The locus of a point P(x, y) such that the distance from P to the line 3x + 4y + 5 = 0 is equal to the distance from P to the origin, is:

A) A parabola B) An ellipse C) A hyperbola D) A circle

29. Find the equation of the locus of a point P(x, y) that moves such that its distance from the point (1, 2) is twice its distance from the point (3, 4).

A) 3x^2 + 3y^2 + 10x + 16y - 43 = 0 B) 3x^2 + 3y^2 - 10x - 16y + 43 = 0 C) x^2 + y^2 + 10x + 16y - 43 = 0 D) x^2 + y^2 - 10x - 16y + 43 = 0

30. What is the locus of a point P(x, y) such that the distance from P to the point (0, 0) is equal to the distance from P to the line y = 4?

A) A parabola x^2 = -8(y - 2) B) A parabola x^2 = 8(y - 2) C) A parabola y^2 = -8(x - 2) D) A parabola y^2 = 8(x - 2)

31. Find the equation of the locus of a point P(x, y) that is equidistant from the point (a, b) and the x-axis.

A) (x - a)^2 + (y - b)^2 = y^2 B) (x - a)^2 + (y - b)^2 = x^2 C) y^2 - 2by + b^2 = (x - a)^2 D) x^2 - 2ax + a^2 = (y - b)^2

32. The locus of a point P(x, y) such that the sum of its distances from (0, 2) and (0, -2) is 8 is:

A) x^2/12 + y^2/16 = 1 B) x^2/16 + y^2/12 = 1 C) x^2/4 + y^2/16 = 1 D) x^2/16 + y^2/4 = 1

33. What is the locus of a point P(x, y) that moves such that its distance from the point (1, 1) is equal to its distance from the line x + y = 0?

A) A parabola B) An ellipse C) A hyperbola D) A circle

34. Find the equation of the locus of a point P(x, y) such that the distance from P to A(1, 0) is equal to its distance from the line x = -1.

A) y^2 = 4x B) y^2 = -4x C) x^2 = 4y D) x^2 = -4y

35. The locus of a point P(x, y) such that the difference of its distances from the points (0, 2) and (0, -2) is 2, is:

A) x^2/1 + y^2/3 = 1 B) x^2/3 + y^2/1 = 1 C) x^2/1 - y^2/3 = 1 D) x^2/3 - y^2/1 = 1

36. What is the locus of a point P(x, y) that moves such that the line segment joining P to the origin is perpendicular to the line segment joining P to the point (5, 0)?

A) A circle with diameter from (0,0) to (5,0) B) A circle with center (2.5, 0) and radius 2.5 C) A parabola D) An ellipse

37. Find the equation of the locus of a point P(x, y) that is equidistant from the point (2, 3) and the line x = 5.

A) y^2 - 6y + 13 = (x - 5)^2 B) x^2 - 10x + 25 = (y - 3)^2 C) y^2 - 6y + 9 = (x - 2)^2 D) y^2 - 6y + 9 = (5 - x)^2

38. The locus of a point P(x, y) such that the sum of its distances from (a, 0) and (-a, 0) is 2c (where c > a), is:

A) x^2/c^2 + y^2/(c^2 - a^2) = 1 B) x^2/(c^2 - a^2) + y^2/c^2 = 1 C) x^2/a^2 + y^2/c^2 = 1 D) x^2/c^2 + y^2/a^2 = 1

39. What is the locus of a point P(x, y) such that the distance from P to the origin is equal to the distance from P to the line y = -4?

A) A parabola x^2 = 8(y + 2) B) A parabola x^2 = -8(y + 2) C) A parabola y^2 = 8(x + 2) D) A parabola y^2 = -8(x + 2)

40. Find the equation of the locus of a point P(x, y) that moves such that its distance from the point (0, 0) is equal to its distance from the line 4x + 3y - 12 = 0.

A) (4x + 3y - 12)^2 = 25(x^2 + y^2) B) (4x + 3y - 12)^2 = 5(x^2 + y^2) C) 25(4x + 3y - 12)^2 = x^2 + y^2 D) 5(4x + 3y - 12)^2 = x^2 + y^2

41. The locus of a point P(x, y) such that the distance from P to (2, 3) is equal to the distance from P to the line y = -1, is:

A) A parabola B) An ellipse C) A hyperbola D) A circle

42. Find the equation of the locus of a point P(x, y) that is equidistant from the y-axis and the point (0, 4).

A) x^2 = -8(y - 2) B) x^2 = 8(y - 2) C) y^2 = -8(x - 2) D) y^2 = 8(x - 2)

43. What is the locus of a point P(x, y) such that the sum of its distances from (3, 0) and (-3, 0) is 10?

A) x^2/25 + y^2/16 = 1 B) x^2/16 + y^2/25 = 1 C) x^2/9 + y^2/10 = 1 D) x^2/10 + y^2/9 = 1

44. The locus of a point P(x, y) such that the distance from P to A(2, 0) is equal to its distance from the y-axis is:

A) y^2 = 4x - 4 B) y^2 = -4x + 4 C) x^2 = 4y - 4 D) x^2 = -4y + 4

45. Find the equation of the locus of a point P(x, y) that moves such that the square of its distance from the origin is equal to its distance from the x-axis.

A) x^2 + y^2 = |y| B) x^2 + y^2 = |x| C) x^2 + y^2 = y D) x^2 + y^2 = x

46. What is the locus of a point P(x, y) such that the distance from P to the point (0, 2) is equal to the distance from P to the line y = -2?

A) x^2 = 8y B) x^2 = -8y C) y^2 = 8x D) y^2 = -8x

47. The locus of a point P(x, y) such that the difference of its distances from the points (2, 0) and (-2, 0) is 2, is:

A) x^2/1 - y^2/3 = 1 B) x^2/3 - y^2/1 = 1 C) x^2/1 + y^2/3 = 1 D) x^2/3 + y^2/1 = 1

48. Find the equation of the locus of a point P(x, y) that is equidistant from the point (0, 0) and the line x = 4.

A) y^2 = -8(x - 2) B) y^2 = 8(x - 2) C) x^2 = -8(y - 2) D) x^2 = 8(y - 2)

49. What is the locus of a point P(x, y) that moves such that the sum of its distances from (0, 3) and (0, -3) is 10?

A) x^2/16 + y^2/25 = 1 B) x^2/25 + y^2/16 = 1 C) x^2/9 + y^2/10 = 1 D) x^2/10 + y^2/9 = 1

50. The locus of a point P(x, y) such that the distance from P to A(1, 0) is equal to its distance from the line x = 5, is:

A) y^2 = -8(x - 3) B) y^2 = 8(x - 3) C) x^2 = -8(y - 3) D) x^2 = 8(y - 3)

Locus and its equation - Online Test

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