i) When a point moves so as to always satisfy a given condition, or conditions, the path it traces out is called its locus under these conditions.
ii) If a point moves according to some given geometrical conditions, then the path traced out by the moving point is called its locus.iii) The locus of a point is the path traced by it, when it moves under a given condition or conditions.
The locus or graph of a equation in two variables is the curve or straight line containing all the points, and only the points whose coordinates satisfy the equation.Fundamental problems of Analytical Geometry
a) Given an equation, to find the corresponding locus.
b) Given a locus under some geometrical condition to determine the corresponding equation.The following properties of the curve will be very helpful in determining the full form of locus equation.
i) Intercept: The intercept of a curve are the directed distances from the origin to the point where the curve cuts coordinates axes.
Fig (1) Fig (2)
Fig (3) Fig (4)
In the figure, OA and OB are the intercepts.
a = OA = intercept on x-axis, b = OB = intercept on y-axis.In figure (1), 'a' and 'b' are both positive.
In figure (2), 'a' is negative and 'b' is positive.In figure (3), 'a' and 'b' are both negative.
In figure (4), 'a' is positive and 'b' is negative.Example:
A point (x, y) moves in such a way that its distance from A (3, -2) is always 6. Find the locus.
Suggested answer:
(This is a circle with centre (3,-2) and radius 6.)
