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is defined to be the distance of the point M from the point 0 prefixed by a sign, plus or minus (the so-called directed distance) according as M belongs to + p or - p, respectively.
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields ...
Take a point P in space, let a be directed distance from yz-plane to P , b be directed distance from xz-plane to P , and c be directed distance from xy-plane to P . We represent the point P by the ordered triple (a, b, c) of real numbers, and we call a, b, and c the coordinates of P .
In this chapter, we will investigate the two-dimensional figures that are formed when a right circular cone is intersected by a plane. We will begin by studying each of three figures created in this manner.
The position of a point P is described by its three directed distances (x, y, z) from each of the coordinate planes. Once the coordinate system is chosen, each ordered set of three numbers uniquely locates a point and conversely, each point has a unique set of coordinates.
Let the directed distance OR x= and the directed distance OS y= . The ordered pair (y) gives us enough information to locate the point x, P. Thus, with every point P in the plane, we can associate an ordered pair of real numbers (x, y) and we say that P has coordinates (x, y). It may be noted that x and y are the directed distances of P from
