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A given line is one of the lines of a pair, or two pairs share a line: find the unknown

This type of question, asked 3 times: 15 May 2023 S2, 26 Apr 2025 S2, 19 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    113
    If one of the lines represented by ax2+2hxy+by2=0ax^2+2hxy+by^2=0 is perpendicular to mx+ny=18mx+ny=18, then

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  2. Question 2

    26 Apr 2025 S2

    123
    If the pair of lines 3x2−5xy+py2=03x^{2}- 5xy+ py^{2}= 0 and 6x2−xy−5y2=06x^{2}-xy- 5y^{2}= 0 have one line common, then p=p =

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  3. Question 3

    19 May 2026 S1

    61
    If one of the lines given by 6x2−xy+4ky2=06x^2 - xy + 4ky^2 = 0 is 3x+4y=03x + 4y = 0, then kk lies in the interval:

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