Algebra/Chapter 17/Loci

The Distance Formula AlgebraChapter 17: Conic SectionsSection 2: Loci of Points Conic Sections 17.2: Loci of Points Up to this point, all of the equations that we have solved or graphed had only one variable in mind. Loci A locus (plural: loci) is one of a set of points which satisfies a set of conditions. The usual result is a curve or a surface. In real life, you likely heard of an object's location. As a matter of fact, the word "location" comes from the word "locus" itself. Loci define where in a plane or space that an object is located. The photo on the right illustrates a set of points (or locus) of the headlights as traced under the condition that all vehicles follow the path of the road. In this analogy: Set of Points: The headlight's locations as seen in the photograph Condition: The road that the vehicles must follow Locus: The lanes in the road as illustrated Unfortunately, there is no general equation for finding loci. However, the following steps are typically used to determine the equation for a locus. Contruct a diagram showing the given information Locate several points that satisfy the rule or condition Draw a curve or line using the located points Write the equation Circles Equidistance Example 17.1: Find the locus of points such that is equidistant from both axes. A point on the x-axis has the coordinates , and a point on the y-axis has the coordinates . Parallel Lines Intersecting Lines