
The path traced by a point moving under a given condition is called its locus.
Definition: A set of all points that satisfy a given geometric condition.
Method to find the equation of the locus of a moving point:
A point moves in a plane so as to remain akways equidistant from two fixed points. A(4, 4) and B(2,8). Find the equation of the locus. Solution: A(4,4) and B(2,8) are the given points. Let P(x,y) be any point on the locus. Using given informations, we getPA = PB PA^{2} = PB^{2} (x+4)^{2} + (y+4)^{2} = (x2)^{2} + (y8)^{2} Simplifying the above we get x+2y3 = 0 This is the required equation of locus. Answer: x+2y3 Directions: Solve the following questions. 