MathDB

Given a set

C

of points in the plane, it is called the distance of a point

P

from the plane to the set

C

at the smallest of the distances from

P

to each of the points of

C

. Let the sets be

C = \{A,B\}

, with

A = (1, 0)

and

B = (2, 0)

; and

C'= \{A',B'\}

with

A' = (0, 1)

and

B' = (0, 7)

, in an orthogonal reference system. Find and draw the set

M

of points in the plane that are equidistant from

C

and

C'

. Study whether the function whose graph is the set

M

previously obtained is derivable.

Problem Statement