How to find equation of the locus of any point

Hi

In mathematics, a locus  is a collection of points which share a property. The term locus is usually used of a condition which defines a continuous figure or figures, that is, a curve. For example, in two-dimensional space a line is the locus of points equidistant from two fixed points or from two parallel lines.

There are different ways of defining locus.

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.

The conic sections may be defined in terms of loci:

• A circle is the locus of points where the distance from a certain point is equidistant to all points on the locus and the distance between the certain point and the locus is called as the radius.
• An ellipse is the locus of points, the sum of the distances from which to the foci is a given value.
• A hyperbola is the locus of points, the difference of the distances from which to the foci is a given value.
• A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.