Answer:
See below
Step-by-step explanation:
I will describe this set in R³. Let P=(x,y,z) be a point equidistant to A and B, that is, the distance from P to A is equal to the distance from P to B.
First, using the usual distance formula, the distance from P to A is equal to
On the other hand, the distance form P to B is equal to
P is equidistant from A and B if and only if P satisfies the equation d(P,A)=d(P,B), that is,
Take the square in both sides of this equation to get
You can simplify using difference of squares and multiplying like this:
which is the equation of a plane.