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Point on a curve nearest to a given point or line

This type of question, asked 2 times: 20 Apr 2025 S1, 17 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S1

    105
    The shortest distance between the line y−x=1y-x= 1 and the curve x=y2x=y^{2} is

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  2. Question 2

    17 Apr 2026 S2

    74
    The coordinates of the points on the curve 4y=x24y = x^2 that are nearest to the point (0,5)(0, 5) are ...

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