What figure is described below?

the points in a plane 4 units from point p.

All points in a plan 4 units from point P
that is a circle
defenition is the set of all points the same distance from a given point

CIRCLE

Ah hah !

-- I take a piece of graph paper and I mark a dot on it.
   I tell you that the name of that point is 'P'.

-- I hand you the pencil, and I tell you to make a dot on the graph
that's 4 units away from point-P.

-- You do it, and you start to hand the pencil back to me.  But
I don't take it.  Instead, I make you keep it, and I tell you mark
another, different point, also 4 units away from 'P'.

-- This goes on all afternoon, and almost until dinner time. 
Every time you make a dot that's 4 units away from 'P', I smile
a little bit, and I tell you to mark another one.

-- Eventually, after you've made a few hundred dots on the paper ...
each and every one of them is 4 units away from point-P ... I hold
up the paper, and I tell you to take 5 steps back and look at it.

What do you see ?

You see a dotted circle.  The center of the circle is the point 'P',
and the radius of the circle is 4 units.