Conic Sections
I don't understand when Spivak says (see the picture)
we can make things a lot simpler for ourselves if we rotate everything so that this intersection line points straight out from the plane of the paper, while the first axis is in the usual position that we are familiar with. The plane $P$ is thus viewed “straight on,” ...
Can someone please clarify it? How does he exactly rotate things to get that view?
The plane $P$ intersects the horizontal plane in a line. In particular, a line within the horizontal plane. Rotate “everything” (that is, space) around the vertical ($z$-) axis so that line rotates to one perpendicular to the $x$-axis. So if you look at the $xz$-plane that line is coming right at you. The intersection of $P$ with the $xz$-plane is the line $L$.