What is locus?

Hint: In these theory based types of questions you should be aware about the geometrical concept of locus such as the formation of locus, what are the geometrical examples of locus this information can help you to have a better approach to the solution to question.

Complete step-by-step solution -
A locus in geometry is an arrangement of all the points which may be a line, a line segment, a curve or a surface, whose position meets or is determined by one or more defined conditions. In certain words, the arrangement or set of points satisfying a certain property is sometimes referred to as the locus of a point satisfying that property. If we have to proof that the geometric shape forms the right locus for a given set of conditions, then the proof is divided into two stages:
(i). We have to prove if all the points which satisfy the conditions are in the form given.
(ii). Now, evidence that the conditions are met by all the points on the given type.
For example, an ellipse is the locus of points which add up to a constant by the distance from two fixed points.

Note: Philosophy of locus: A geometrical form e.g. curve was not regarded as an infinite set of points until the beginning of the 20th century, instead , it was regarded as an object on which a point can be placed or on which it moves. Thus, a circle in the Euclidean plane was defined as the locus of a point at a fixed point distance, the center of the circle. Once set theory became the universal foundation upon which all the mathematics is built, the term locus became rather old- fashioned.