JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Self Evaluation Test - Complex Numbers and Quadratic Equations

  • question_answer
    The locus of a point in the Argand plane that moves satisfying the equation \[|z-1+i|-|z-2-i|=3:\]

    A) is a circle with radius 3 and centre at \[z=\frac{3}{2}\]

    B) is an ellipse with its foci at \[1-i\] and \[2+i\] and major axis \[=3\]

    C) is a hyperbola with its foci at \[1-i\] and \[2+i\]and its transverse axis \[=3\]

    D) None of the above

    Correct Answer: C

    Solution :

    The given eq. implies that the difference between the distances of the moving point from two fixed points (1 - i) and (2 + i) is constant using the property of the hyperbola that the difference between the focal distances of any point on the curve is constant, the locus in reference is therefore a hyperbola.


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