TopLocus is defined as a curve that is achieved when some Point moves in the space according to certain conditions. So, the curve we obtain can be called as a collection of points each of which satisfying the given conditions or we can also say that every point satisfying the given conditions are supposed to lie on this curve. For any expression or relation H (x, y) = 0 such that every point lying on the locus satisfies this equation, then it is called as the equation of the locus. So, let us learn how to find the locus of any point in the space through an example:
Example: How to find the equation for locus of a point whose distance from a point equals its distance from y axis?
Solution: Given condition to find the locus of a point whose distance from y – axis equals to the distance from other point. It is clear from the given condition that the point whose locus has to be found lies between the y – axis and other point. To maintain an equal distance from the y – axis and the other point, required point must lie in a line such that its distance from the y – axis and the point to the right or to the left remains constant
Also this line has to be parallel to the y – axis and perpendicular to the x – axis. So, this will make an intercept on the x – axis and its equation can be given as: x = c, where 'c' is the distance that the point maintains from y – axis and other point. Suppose the distance between the line parallel to y- axis is 4 units then equation of line can be given as x = 4.