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Joint equation of the lines through the origin making a given angle with a given line

The same question, asked 5 times: 4 May 2023 S2, 9 May 2023 S2*, 10 May 2024 S2*, 13 Apr 2026 S1, 16 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    112
    The combined equation of two lines through the origin and making an angle of 45° with the line 3x+y=03x+y=0, is

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  2. Question 2

    9 May 2023 S2

    135
    The joint equation of pair of lines through the origin and making an angle of π6\frac{\pi}{6} with the line 3x+y−6=03x+y-6=0 is

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  3. Question 3

    10 May 2024 S2

    104
    The joint equation of a pair of lines passing through the origin and making an angle of π4\frac{\pi}{4} with the line 3x+2y−8=03x+2y-8=0 is

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  4. Question 4

    13 Apr 2026 S1

    56
    The joint equation of the pair of lines through the origin and making an angle of π4\dfrac{\pi}{4} with the line 3x+y−6=03x + y - 6 = 0 is

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  5. Question 5

    16 Apr 2026 S2

    57
    The combined equation of the pair of lines passing through the origin and making an angle π4\dfrac{\pi}{4} with the line 3x+y−6=03x + y - 6 = 0 is...

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