MathDB

Two points

A

and

B

are given in the plane. A point

X

is called their preposterous midpoint if there is a Cartesian coordinate system in the plane such that the coordinates of

A

and

B

in this system are non-negative, the abscissa of

X

is the geometric mean of the abscissae of

A

and

B

, and the ordinate of

X

is the geometric mean of the ordinates of

A

and

B

. Find the locus of all the preposterous midpoints of

A

and

B

.
(K. Tyschu)

Problem Statement