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.
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 {√(a^{2} - b^{2}), 0} and S’ {- √(a^{2} - b^{2}), 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 isAnswers for the worksheet on locus are given below to check the exact answers of the above questions on math locus.
Answers:
1. 5x - y = 11.
2. x^{2}/36 + y^{2}/27 = 1, Ellipse.● Locus
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