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Tangent to a parabola with a given slope (y = mx + a/m)

This type of question, asked 3 times: 15 May 2023 S1, 22 Apr 2025 S1, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    15 May 2023 S1

    142
    The equation of the tangent to the parabola y2=8xy^{2}=8x, which is parallel to the line 4x−y+3=04x-y+3=0 is

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  2. Question 2

    22 Apr 2025 S1

    144
    The line y=mx+3y=mx+ 3 is tangent to the parabola y2=4xy^{2}= 4x, if the value of m is

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  3. Question 3

    15 May 2026 S1

    59
    The tangent to the parabola x2=2yx^2 = 2y at point P makes an angle of 45∘45^\circ with the X-axis, then the coordinates of P are:

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