( 42.5)

To solve this efficiently, we can use the property of the locus of a complex number .
The equation represents a circle only if is greater than or equal to a specific minimum value. This minimum occurs when is the midpoint of the line segment joining and .

Identify the points

From the equation :

Find the distance between and

Let be the distance between these two points:

Apply the Condition

For the equation to represent a circle (including a point circle), must be at least half the square of the distance between the two fixed points:

Substituting the value of :

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