|The path traced by a point moving under a given condition is called its locus. |
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
PA2 = PB2
(x+4)2 + (y+4)2 = (x-2)2 + (y-8)2
Simplifying the above we get
x+2y-3 = 0
This is the required equation of locus.
Directions: Solve the following questions.