44 
Proceedings of Royal Society of Edinlurgh [sess. 
where 
= OW^ = + ^ab cos w ; 
and thus the focus. 
Since - ay = 0 is a diameter, the directrix is 
x{a + h cos (jo) + y{h + a cos w) - = 0 , 
being perpendicular to a diameter ; and fx is found at once, since 
the perpendicular from 0 on MM' =OS cos w. Thus, observing 
that 
(a + 5 cos (of + {h + a cos wf - 2(a + 6 cos a>)(6 + a cos w) cos co = c^sin^ 
we have 
tx a&coso) , 
- = (Jb COS CO = , and ix = ab cos co , 
c c ’ 
which gives the directrix. 
The axis is bx-ay -X = 0 and A is most easily found by the 
condition that the focus is on the line. Thus 
A = a6(&2-a2)/c2, 
and hence the axis. 
