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Normal to y = x log x parallel to a given line: point or equation

This type of question, asked 4 times: 2 May 2023 S2, 10 May 2023 S1, 16 May 2023 S2, 15 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    113
    The co-ordinates of a point on the curve y=xlog⁡xy = x\log x at which the normal is parallel to the line 2x−2y=32x - 2y = 3 are

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  2. Question 2

    10 May 2023 S1

    132
    The equation of the normal to the curve y=xlog⁡xy=x\log x, which is parallel to the line 2x−2y+3=02x-2y+3=0, is

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  3. Question 3

    16 May 2023 S2

    137
    The equation of the normal to the curve y=xlog⁡xy = x\log x parallel to 2x−2y+3=02x-2y+3=0 is

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  4. Question 4

    15 Apr 2026 S1

    75
    The co-ordinates of the point on the curve y=xlog⁡xy = x\log x at which the normal is parallel to the line 2x−2y=32x - 2y = 3 are...

    Tap an option to check your answer.