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Joint equation of the lines through a point perpendicular to a given pair

The same question, asked 2 times: 11 May 2024 S2*, 14 May 2026 S1. Every wording below, oldest first.

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  1. Question 1

    11 May 2024 S2

    147
    The joint equation of the pair of lines passing through the point (3,−2)(3,-2) and perpendicular to the lines 5x2+2xy−3y2=05x^2+2xy-3y^2=0, is

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  2. Question 2

    14 May 2026 S1

    58
    The joint equation of pair of lines passing through origin and perpendicular to the lines given by 3x2+4xy−5y2=03x^2 + 4xy - 5y^2 = 0 is

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