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Tangent or normal at the point where a curve crosses an axis

This type of question, asked 4 times: 2 May 2023 S1, 4 May 2023 S2, 26 Apr 2025 S1, 26 Apr 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    148
    The normal to the curve y(x−2)(x−3)=x+6y(x-2)(x-3) = x+6 at the point, where the curve intersects the Y-axis, passes through the point

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  2. Question 2

    4 May 2023 S2

    144
    The equation of the tangent to the curve y=1−ex/3y=1-e^{x/3} at the point of intersection with Y-axis is

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  3. Question 3

    26 Apr 2025 S1

    135
    The equation of the tangent to the curve (1+x2)y=2−x\left( 1 +x^{2} \right)y= 2 -x, where it crosses the X -axis, is

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  4. Question 4

    26 Apr 2025 S2

    150
    The equation of the tangent to the curve y=be−x/ay=be^{-x/a} at the point where it crosses the Y axis is

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