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Condition or parameter for three lines to be concurrent

This type of question, asked 2 times: May 2021 S1, 12 May 2024 S2. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    105
    The three straight lines ax+by=cax+by=c, bx+cy=abx+cy=a and cx+ay=bcx+ay=b are collinear if

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  2. Question 2

    12 May 2024 S2

    112
    If kik_i are possible values of kk for which lines kx+2y+2=0,  2x+ky+3=0kx+2y+2=0,\; 2x+ky+3=0 and 3x+3y+k=03x+3y+k=0 are concurrent, then ∑ki\sum k_i has the value

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