Relative Positions Between the Hyperplane and the n-Sphere

This paper discusses are some topics Analytic Geometry, studied in basic education in the context of Euclidean space $ n $-dimensional. Presents itself for example, the concepts of hyperplane and $(n-1)$-sphere, which correspond to the high school to the circle and line, respectively. And in the said geometry are studied the relative positions between line and circumference. Similarly, we study the relative positions between the hyperplane and the $(n-1)$-sphere in this space. In this context, it presents a theorem that characterizes the relative positions.