Also  by  giving  a  suitable  value  to  I  the  equation  u  +  lwz  =  0
may  be  made  to  represent  the  two  straight  lines  which  touch
the  conic  section  u  =  0  at  the  points  where  it  intersects  the
straight  line  w  =  0.  This  may  be  inferred  from  Art.  293  ;

/yi  ni

the  equation  w  =  0  is  equivalent  to  j-  +  ~  —  1  =  0,  and  the
equation  u  =  0  is  equivalent  to  I  j  +  ~  —  1  j  4-  pxy  =  0.    Thus


by  taking  I  —  —  1  we  have  u  +  lw*  =  iujcy\  and  the  equation
xy  =  0  denotes  the  two  tangents  to  the  conic  section  u  =  0  at
its  points  of  intersection  with  the  straight  line  w  =  0.
342.  Pascal's  Theorem.  The  three  intersections  of  the
opposite  sides  of  any  hexagon  inscribed  in  a  conic  section  are
on  one  straight  line.
