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Circle on AB as diameter where A, B have coordinates given by roots of two quadratics

The same question, asked 2 times: 10 May 2023 S1, 13 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    109
    The abscissae of the two points A and B are the roots of the equation x2+2ax−b2=0x^2+2ax-b^2=0 and their ordinates are roots of the equation y2+2py−q2=0y^2+2py-q^2=0. Then the equation of the circle with AB as diameter is given by

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  2. Question 2

    13 May 2024 S2

    148
    The abscissae of two points A and B are the roots of the equation x2+2ax−b2=0x^2+2ax-b^2=0 and their ordinates are roots of the equation y2+2py−q2=0y^2+2py-q^2=0. Then the equation of the circle with AB as diameter is given by

    Tap an option to check your answer.