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    Question

    The equation∣ z-2i ∣ + ∣ z + 2i ∣ = 6

    represents:
    A A circle Correct Answer Incorrect Answer
    B An ellipse Correct Answer Incorrect Answer
    C A parabola Correct Answer Incorrect Answer
    D A straight line Correct Answer Incorrect Answer

    Solution

    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 .

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