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Message-ID: <UfRaT_600WB6MhT4BC@andrew.cmu.edu>
Date: Mon,  8 Feb 1993 09:01:46 -0500 
From: John Robert Leavitt <jl3j+@andrew.cmu.edu>
Subject: Re: Straight Lines on a Polar Coordinate Plotter - Help Please !
Lines: 33

From my old high school analytic geometry book:

"The general equation of first degree in x and y is ax + by = c.  To
find the corresponding equation in polar coordinated, x may be
replaced by \rho cos \theta and y by \rho sin \theta.  Thus

              a \rho cos \theta + b \rho sin \theta = c

or
                                 c
(4.10)       \rho = ---------------------------
                    a cos \theta + b sin \theta

is its polar equation.

There are three special cases.  In terms of ax + by = c, they are as follows:

1. c = 0 and both a and b are not equal to 0.  The graph of this
   equation is a line passing through the origin.  In polar form its
   equation is \theta = k, where k is constant.

2. a =/= 0 and b = 0. The equation becomes ax = c and is graphed as a
   line parallel to the y axis.  If the x intercept of such a line is
   d, its equation is x = d; then its polar form is
   \rho cos \theta = d.


3. a = 0 and b =/= 0.  The equation becomes by = c and is graphed as a
   line parallel to the x axis.  If such a line has a y intercept e,
   its equation is y = e and in polar form is \rho sin \theta = e."


           - "Analytic Geometry", Middlemiss, Marks, and Smart, p. 117
