18 
In the case A,,< 0 we prefer to write a A. Des 
v2 
\ 
it 
=—+Y—A,,.s f Ay ah d for ch 
=| LE me or V DE and cos —- 2 OL = Fi 
So, whilst the formulae (89) are specially suitable for the ellipse 
we do better in using for the hyperbola 
22 eg 
A . Aa eas V —A,, sin — 
Ut V2 
A, cos PV 
2 ENE 
2 Ae 
y == 5 (ane VY —A,, . SUN an 
it V2 
A: COS“ — 
2 5 | 
Consequently the real points of the hyperbola correspond to purely 
imaginary values of t. 
Case IV®. Putting r,=—=0, (705) (4 comm. p. 1017) we find 
PE 3/2 th en SS ee 
V2 
and therefore 
3 
[= — 
T 
ch? — 
V2 
So the formulae (62) and (63) now give 
OAs 2 asss T 
=d st At en 
g 13 aie 23 zin 33 oT 2 2 ’ 
Le. 
ee 2 
CO i Bh Tee 
and 
E 
Ast Ary V2Àge Dae = —= Va A.z.sh—, 
so we find 
dz Van | “i Oss Âis I? z 9 | 
oe A Pa oe oh C 2 4 
Zs (90) 
= Sia Gan eon tag Se eo 
A va 2A we ee 
Case IV¢. Here we have : 
ey 
