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Tangent or normal parallel to a given line: points or equation

This type of question, asked 4 times: 12 May 2024 S2, 19 Apr 2025 S2, 12 May 2026 S1, 12 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    12 May 2024 S2

    132
    The equation of the normal to the curve 3x2−y2=83x^2 - y^2 = 8, which is parallel to the line x+3y=10x + 3y = 10, is

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  2. Question 2

    19 Apr 2025 S2

    145
    The equation of tangent to the curve y=cos⁡(x+y)y= \cos(x+y) where −2π≤x≤2π- 2\pi\leq x\leq 2\pi and.which is parallel to the line x+2y=0x+ 2y= 0, is

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  3. Question 3

    12 May 2026 S1

    75
    The sum of abscissa of the points on the curve y=x3−3x2+x−2y = x^3 - 3x^2 + x - 2 at which the tangent is parallel to the line y=xy = x is ___

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  4. Question 4

    12 May 2026 S2

    76
    The sum of the abscissae of the points on the curve y=x3−6x2+x+3y = x^3 - 6x^2 + x + 3 whose normal is parallel to the line x+y=1975x + y = 1975 is...

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