1456 
of differentiation we find 2 yp 82", so that the tangent becomes: 
r 
‘ 
the latter cuts the a-axis in the point N= oe The length of the 
tangent between the point, of contact and the intersection with the 
x-axis becomes therefore V 4 x2? + 7°, or V 4a? Ha’, and if we now 
take this length as z-coordinate, and call it &, and put thus: 
the point (8,8) is a point of the nodal curve. The equation of this 
curve becomes therefore: 
GP == 46" 27:5", 
and this curve has apparently a node in QO, while the nodal tangents 
enclose with 3 an angle whose tangent is determined by 
tS 
lim. — == = 2. 
E=0 § 
Besides in O it cuts the v-axis moreover in the point § = ET 
it consists therefore of two infinite branches and a knot, and now 
the knot is parasitic; the circles representing the points of this knot 
cyclographically are of course real indeed, but they do not cut the 
curve 7? =«? really, at least not really orthogonally. 
3 4 ; ; nt 
$ 4. The point §=— Dn has its meaning too, for this simple 
7 
example as well as in the general case; we will just illustrate it 
therefore. If the tangent 
: DS en 
i= — (X—.2) 
2y 
; _ da? 5 na 
will become isotropic, — must be = 7, consequently 32? = 277. From 
2y 
; 4 8 
this equation and y7=2* we find «= — —, y= —,, and if the 
E Oe, 27% 
tangent in this point is intersected with the a-axis, we find «= — 
dr 
zn the point Zien therefore a focus of y? =, and the 
parasitic knot of the nodal curve extends between the cusp and the 
focus. 
