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Lines through a point making a given angle with a given line

This type of question, asked 3 times: May 2022 S1, 11 May 2023 S2, 15 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    142
    The equations of the lines passing through the point (3,2)(3, 2) and making an acute angle of 45° with the line x−2y−3=0x - 2y - 3 = 0 are

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  2. Question 2

    11 May 2023 S2

    137
    A straight line L through the point (3,−2)(3,-2) is inclined at an angle of 60°60° to the line 3x+y=1\sqrt{3}x+y=1. If L also intersects the X-axis, then the equation of L is

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  3. Question 3

    15 May 2026 S2

    61
    The equations of the lines passing through the center of circle x2+y2−4x−10y−7=0x^2 + y^2 - 4x - 10y - 7 = 0 and intersecting the line 3x−y−1=03x - y - 1 = 0 at an angle π4\dfrac{\pi}{4} is...

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