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Sign conditions on a and b when ax + by + c = 0 is a normal to xy = 1

The same question, asked 3 times: 10 May 2024 S1, 13 Apr 2026 S1*, 20 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S1

    127
    If αx+by+c=0\alpha x+by+c=0 is normal to curve xy=1xy=1, then

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  2. Question 2

    13 Apr 2026 S1

    74
    The equation of the normal to the curve xy+7=0xy + 7 = 0 is Ax+By+C=0Ax + By + C = 0, then

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  3. Question 3

    20 Apr 2026 S1

    75
    If the line ax+by+5=0ax + by + 5 = 0 is a normal to the curve xy=1xy = 1 then .....

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