258 



I. The directrix DS of the parabola is an asymptote of the curve, 

 which has two infinite branches along this line above and below the 

 axis. These branches intersect at right angles on the axis of the 

 parabola in its vertex, and form an oval or loop between this point 

 and the focus of the parabola F. 



II. The radius vector r=a (sec + tan 0), drawn from the focus F 

 of the parabola, cuts the loop and one of the infinite branches in the 

 points R! and R, so that 



FR=(sec 0+tan 0), and FR,=a(sec tan 0). 

 The product of the segments of this secant, as in the circle, is con- 

 stant and equal to a 2 . 



These points may be named Reciprocal Points. 



