Worksheet on Locus of a Moving Point

To practice the questions given in the worksheet on locus of a moving point we need to follow the method of obtaining the equation of the locus to solve these questions.

1. A point moves in such a manner that three times of its abscissa is greater by 5 than two times of its ordinate; find the equation of its locus.

2. If twice the abscissa of a point moving in the xy-plane always exceeds three times its ordinate by 1, show that the locus of the point is a straight line.

3. A point moves in the xy-plane in such a way that its distance from the x-axis and the point (1, -2) are always equal. Find the equation of its locus.

4. A point moves in the xy-plane in such a way that its distance from the point (4, 0) is always equal to its distance from the y-axis. Find the equation to the locus of the moving point.

5. A point moves such that its distance from the y –axis is equal to its distance from the point (2, 0). Find its locus and identify the nature of the conic.

6. A point P (x, y) moves in the xy-plane in such a way that its distance from the point (0, 4) is equal to 2/3 rds of its distance from the x-axis ; find the equation to the locus of P.

7. Find the equation to the locus of a moving point which is equidistant from the points (2,3) and (4,-1).

8. Find the locus of a point which moves so that the sum of the squares of its distance from the points (3, 0) and (-3, 0) is always equal to 50.

9. A point moves in a plane such that its distance from the point (2, 3) exceeds its distance from the y-axis by 2. Find the equation to the locus of the point.

10. A point so moves that the sum of squares of its distance from (a, 0) and (-a, 0) is 2b². Find the equation to the locus of the moving point. If a = b then what will be locus of the moving point?

11. The ratio of the distance of a moving point from the points (3, 4) and (1, -2) is 2 : 3; find the locus of the moving point.

12. A (1, 2) and B (5, -2) are two given points on the ey-planes, on which C is a moving point, such that the numerical value of the area of ΔCAB is 12 square units. Find the equation to the locus of C.

Answers for the worksheet on locus of a moving point are given below to check the exact answers of the above questions on locus.

Answers:

1. 3x – 2y = 5.

3. x² – 2x + 4y + 5 = 0.

4. y² = 8 (x – 2).

5. y² = 4(x – 1), parabola.

6. 9x² + 5y² – 72y + 144 = 0.

7. x – 2y = 1.

8. x² + y² = 16.

9. (y – 3)² = 8x.

10. x² + y² = b² – a²; x² + y² = 0 i.e., the moving point represent the origin.

11. 5x² + 5y² – 46x – 88y + 205 = 0.

12. x + y = 9 or, x + y + 3 = 0.

● Locus