line equations
POLAR EQUATION OF A LINE

Lines through the pole have constant equations:

θ = k ,

where k is the angle in readians measured
in a counter clockwise direction fron the
ray starting at the pole and directed
to the right ( θ = 0 ) rotated
to the line ( with θ = k ).


For Other Straight Lines:

r = p sec( θ - ω )

where p is the closest distance from the
pole (point O) to the line ( @ point P),
theta is defined as above and omega is
the angle in radians from the initial ray
for which θ = 0 in a counterclock wise
direction to the line segment OP.




RATE OF CHANGE FOR A STRAIGHT LINE:

Show that dr/dθ (for θ ≠ k, a constant ) is an equation of a parabola.

The graph of this parabola has has an axes of symmetry
through the pole and is in the same direction as its line!


Where is the vertex and focus of this parabola?


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William V. Thayer, PedLog