1. ANALYTIC GEOMETRY
LESSON 54: TANGENTS FROM EXTERNAL POINT
Essentially the same techniques may be used from dealing with
this type of problem.
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2. ANALYTIC GEOMETRY
POLAR COORDINATES
LESSON 55: POLAR COORDINATES
The polar coordinate system makes use of this method of describing
the location of a point on a plane. From the given fixed point, which is called
the pole of origin, a reference line is drawn (generally in a horizontal
direction 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. Hence
the polar axis is unusually also letter OX. The distance r of any point P from
O is called its radius vector and its direction θ from OX is called its polar
angle. 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 when
measured clockwise.
b. r is positive if laid off on the terminal side of θ, negative if laid off
on 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.
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3. ANALYTIC GEOMETRY
Central Colleges of the Philippines