# Worksheet on Locus

To practice the questions given in the worksheet on locus math we need to read the questions carefully and then follow the method of obtaining the equation of the point of a locus to solve these questions.

1. A point moves is always collinear with the points (2,-1) and (3, 4); find the equation to the locus of the moving point.

2. The sum of the distance of a moving points from the points (3, 0) and (-3, 0) is always equal to 12. Find the equation to the locus and identify the conic represented by the equation.

3. Find the equation to the locus of a moving point which moves in such a way that the difference of its distance from the points (5, 0) and (-5, 0) is always 5units.

4. Find the equation to the locus of a moving point which is equidistant from the point (2a, 2b) and (2c, 2d). Interpret geometrically the equation to the locus.

5. The variable straight line x/a + y/b = 1, is such that a + b = 10. Find the locus of the middle point of that part of the line, which is intercepted between the axes.

6. The sum of the intercepted cut off from the co-ordinate axes by a variable line is 14 units. Find the locus of the point which divides internally the portion of the line intercepted between the co-ordinate axes in the ratio 3 : 4.

7. The co-ordinate of a moving point P are (at2, 2at) where t is a variable parameter. Find the equation to the locus of P.

8. If θ is a variable, find the equation to the locus of a moving point whose co-ordinate are (a sec θ, b tan θ).

9. The co-ordinate of a moving point P are (ct + c/t, ct – c/t), where t is a variable parameter. Find the equation to the locus of P.

10. S {√(a2 - b2), 0} and S’ {- √(a2 - b2), 0} are two given point and P is a moving point in the xy-plane such that SP + S’P = 2a. Find the equation to the locus of P.

11. The co-ordinate of a moving point P are

{(2t + 1)/(3t – 1), (t – 1)/(t + 1)}, where t is a variable parameter. Find the equation to the locus of P.

11. The co-ordinate of a moving point P are [3(cot θ + tan θ), 4(cot θ - tan θ)] where is a variable parameter. Show that the equation to the locus P is

x2/36 – y2/64 = 1.

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

1. 5x - y = 11.

2. x2/36 + y2/27 = 1, Ellipse.

3. 12x2 - 4y2 = 75.

4. (a - c)x + (b – d)y = a2 + b2 - c2 - d2; Perpendicular bisector of the line segment joining the given point.

5. x + y = 5.

6. 3x + 4y = 24.

7. y2 = 4ax.

8. x2/a2 - y2/b2 = 1.

9. x2 - y2 = 4c2.

10. x2/a2 + y2/b2 = 1.

11. 5xy + x - y = 3.

Locus

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