Answer-The equation∣ z-2i ∣ + ∣ z + 2i ∣ = 6 represents:

This matches the general form Sum of distances from two fixed points is constant This is the standard definition of an ellipse . In an ellipse The sum of distances from any point on the ellipse to the two foci is constant. Here The two fixed points are at 0,2 and 0,2, And the constant sum is 6. Thus, the given equation represents an ellipse .