It can be solved by "eyeballing" the problem if you know a particular theorem.
We have:, where represents a circle. .How?
The distance is proportional to the distance .
By definition, the locus of is a Circle of Apollonius.
also simplifying the eqn. we get
. . . not quite
which makes the constt. term +ve, hence makes the circle real. Am I OK?
We have: .
. . .Or: .
And we see the restrictions on the constants.
But equally important, the right side must be positive.
Hence: . and
. . . or: . and