This question is from the chapter 1 of Reid's note: Chapters on algebraic surfaces
Suppose that L:(x=y=0), M:(z=t=0), and L$_5$:(y=t=0) lie on a nonsingular cubic surface X in P$^3$, define a morphism X$\to$ P$^2$ as (x:y:z:t)$\in$(xt:yz:yt), it seems that this morphism blows up 6 points on P$^2$, we can get the cubic surface, but it is hard for me to imagine what it looks like.
Where is the 6 points and what is the equations of the fibre lines from the 6 points?