Two subsets of the plane? 
Aren't planes described by $(x,y,z)$?
I know that the point (2,0) satisfies a, and the point (1.5,4) satisfies b. But how would I turn these into equations and geometric descriptions?
I'm stuck.

Hint: Using the distance formula, a point $(x,y)$ will satisfy a) exactly when
$$ 
\sqrt{(x-4)^2 + y^2} =  2\sqrt{(x-1)^2 + y^2} = 1
$$
and it will satisfy b) if
$$
|x+1| =  \sqrt{(x-2)^2 + (y-4)^2}
$$
However, both of these equations can be simplified. 
