Example of Line at infinity in Miles' Book

Question

Background: I've started reading Miles' "Undergraduate Algebraic Geometry" (Link) recently though struggling a lot. \

Please allow me to just paste the example on Page 23 as follows;

I have visualised each example as follows;

• (a): https://www.geogebra.org/3d/mfek26ph
• (b): https://www.geogebra.org/3d/z5uxh9e6

In both cases, the intersection points (e.g., $(a, \pm b, 0), (0, 1, 0)$) are the projective coordinates, i.e.,, points along a ray can be representative by a point, right?