588 
389] 
27 
igh 
we 
the 
¡nts 
iose 
the 
rite 
the 
the ON A LOCUS DERIVED FROM TWO CONICS. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. viii. (1867), 
pp. 77—84.] 
the 
Required the locus of a point which is such that the pencil formed by the 
tangents through it to two given conics has a given anharmonic ratio. 
Suppose, for a moment, that the equation of the tangents to the first conic is 
(x — ay) (,x — by) = 0, and that of the tangents to the second conic is (x — cy) (x — dy) = 0, 
and write 
A = (a — b) (c — d), 
B =(a — c)(d - b), 
so that 
write also 
G = (a — d)(b — c), 
A + B + C = 0, 
A 
G 
A ’ 
then the anharmonic ratio of the pencil will have a given value k if 
in 
hat 
that is, if 
(k-h) (k — k. 2 ) = 0 ; 
i a 
, 7 BG n 
nal 
№ + k + = 0, 
3ns 
or, what is the same thing, if 
tnd 
the 
;he 
that is, if 
A*(2k + iy + *BC-A*=0; 
A 2 (2k + l) 2 — (B-G) 2 =0, 
4—2