1. loci

How many points are there in a plane that are 4 centimeters from a given line and also 5 centimeters from a given point on that line?

Did you make a sketch?

How many points are there in a plane that are 4 cm from a given line
and also 5 cm from a given point on that line?

All points which are 4 cm from line $L$ are on a pair of lines
. . parallel to and 4 cm from line $L.$
Code:
  - - - - - - - - - - - - - -
:
4
:
---------------------------- L
:
4
:
- - - - - - - - - - - - - -

Given a point P on line L, there are four points
. . which are on the two lines and 5 cm from P.
Code:
  - - - - o - - - o - - - -
:        \     /
4        5\   /5
:          \ /
-------------*------------ L
:          /P\
4        5/   \5
:        /     \
- - - - o - - - o - - - -