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Condition for a second-degree equation to represent a pair of lines: find the unknown

This type of question, asked 4 times: 9 May 2023 S1, 10 May 2024 S1, 20 Apr 2025 S2, 15 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    143
    If an equation hxy+gx+fy+c=0hxy+gx+fy+c=0 represents a pair of lines, then

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  2. Question 2

    10 May 2024 S1

    122
    Number of integral values of p in [-5,5] such that 2x2+4xy−py2+4x+qy+1=02x^2+4xy-py^2+4x+qy+1=0 represents a pair of lines

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  3. Question 3

    20 Apr 2025 S2

    114
    If the equation kxy+10x+8y+16=0kxy+ 10x+ 8y+ 16 = 0 represents a pair of lines, then

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  4. Question 4

    15 May 2026 S1

    57
    If the equation mx2−y2+2y+n=3mx^2 - y^2 + 2y + n = 3 represents a pair of perpendicular lines, then the values of mm and nn respectively are...

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