The elements of coordinate geometry, by S. L. Loney, M.A.

CHAPTER V.

THE STRAIGHT LINE (continued).
POLAR EQUATIONS. OBLIQUE COORDINATES.
MISCELLANEOUS PROBLEMS. LOCI.
88. To find the general equation to a straight lina in
polar coordinates.
Let p be the length of the perpendicular OY from the
origin upon the straight line, and
let this perpendicular make an
angle a with the initial line.
Let P be any point on the B
line and let its coordinates be r \
and 0. A
The equation required will
then be the relation between r, 0, p, and a.
From the triangle OYP we have
p = r cos YOP = r cos (a - 6) = r cos (0 - a).
The required equation is therefore
r cos (O - a) =p.
[On transforming to Cartesian coordinates this equation becomes
the equation of Art. 53.]
89. To find the polar equation of the straight line
joining the points whose coordinates are (re, 01) and (r2, 02).