# Descriptive Geometry/Cone Loci

## Definition

A locus(loci) is a solution(s) that satisfy a given set of conditions. [[[[Media:|thumbnail]]]] Depending on the situation, the locus can be a different solution. In Figure A, there is a vertical axis BO and a point a. When point a is revolved around BO, the path that point a creates is a circle. In this given set of conditions, the locus is the circular path that point a creates when revolved around BO because that circle is a collection of all the points that are the same distance from BO as point a. In Figure B, there is a vertical axis BO with a line segment AO touches BO to creates ∠AOB. When AO is revolved around BO, the path that the AO creates a surface that takes the shape of a cone. Therefore, in this particular set of conditions, the locus AO is a conical surface because that surface is a collection of all the line segments that can be represented by AO in a three-dimensional space.

The locus of two intersecting objects would be all the solutions that satisfy the intersection. In the case if cone "A" and cone "B" shared a vertex and had the same slant height, there are three possible solutions: 1 intersection, 2 intersections, or none. If the angle between the two axis is less than the sum of the two vertex angles, there are two locus intersection solutions. If the angle between the two axis is equal to the sum of the two vertex angles, there is only one solution. If the angle between the two axis is greater than the sum of the two vertex angles, there are no solutions.