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Lesson54 55


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Lesson54 55

  1. 1. ANALYTIC GEOMETRYLESSON 54: TANGENTS FROM EXTERNAL POINT Essentially the same techniques may be used from dealing withthis type of problem.Central Colleges of the Philippines
  2. 2. ANALYTIC GEOMETRYPOLAR COORDINATESLESSON 55: POLAR COORDINATES The polar coordinate system makes use of this method of describingthe location of a point on a plane. From the given fixed point, which is calledthe pole of origin, a reference line is drawn (generally in a horizontaldirection to the right). This is called the initial line or the polar axis and,when so drawn, coincides with the right half of the Cartesian x-axis. Hencethe polar axis is unusually also letter OX. The distance r of any point P fromO is called its radius vector and its direction θ from OX is called its polarangle. The radius vector and the polar angle are the polar coordinates (r,θ) of the point. The sign conventions are: a. θ is positive when measured counterclockwise, negative whenmeasured clockwise. b. r is positive if laid off on the terminal side of θ, negative if laid offon the prolongation through O of the terminal side.The following important features of the polar coordinates system 1. Every pair of polar coordinates represents one and only one point. 2. Every point may be represented by an infinite number of pairs of polar coordinates.Central Colleges of the Philippines
  3. 3. ANALYTIC GEOMETRYCentral Colleges of the Philippines