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

256

COORDINATE GEOMETRY.

Cor. 1. The points on the auxiliary circle corresponding to P and D subtend a right angle at the centre.
For if p and d be these points then, by Art. 258, we
have
LpCA':= and _ dCA' = '.
Hence
LpCd = LdCA'- LpCA' = - '= 90~.
Cor. 2. In the figure of Art. 286 if P be the point 4,
then D is the point 4 +-90~ and D' is the point > - 90~.
285. From the previous article it follows that if P be
the point (a cos 4, b sin 4), then D is the point
{a cos (90~ + /), b sin (90~ + 0)} i. e. (- a sin 4, b cos ).
Hence, if PN and DM be the ordinates of P and D,
we have
NP CMa CON MD
b a ' a b
286. If PCP' and DCD' be a pair of conjugate diameters, then (1) CP2 + CD2 is constant, and (2) the area of
the parallelogram fornted by the tangents at the ends of these
diameters is constant.