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Joint equation of two lines through a point with given inclinations

This type of question, asked 5 times: May 2022 S1, 11 May 2023 S1, 11 May 2023 S2, 23 Apr 2025 S1, 17 Apr 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    107
    The joint equation of pair of lines through the origin and making an equilateral triangle with the line y=5y = 5 is

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  2. Question 2

    11 May 2023 S1

    139
    The joint equation of two lines through the origin, each making an angle with measure of 30∘30^\circ with the positive Y-axis, is

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  3. Question 3

    11 May 2023 S2

    130
    The joint equation of pair of lines through the origin, each of which makes an angle of 30°30° with Y-axis, is

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  4. Question 4

    23 Apr 2025 S1

    104
    The joint equation of two lines passing through (−2,3)( - 2,3) and parallel to the bisectors of the angle between the co-ordinate axes is

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  5. Question 5

    17 Apr 2026 S1

    57
    The joint equation of a pair of lines passing through point (1,4)(1, 4), one of which is parallel to X-axis and the other makes an angle of 45∘45^\circ with the positive direction of X-axis, is

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