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Lines through the origin trisecting the part of a line between the axes

This type of question, asked 2 times: 6 Apr 2023, 27 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    6 Apr 2023

    66
    The straight lines l1l_{1} and l2l_{2} pass through the origin and trisect the line segment of the line L: 9x+5y=459x + 5y = 45 between the axes. If m1m_{1} and m2m_{2} are the slopes of the lines l1l_{1} and l2l_{2},then the point of intersection of the line y=(m1+m2)xy =\left( m_{1}+m_{2} \right)x with LL lies on

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  2. Question 2

    27 Jan 2024

    76
    The portion of the line 4x+5y=204x + 5y = 20 in the first quadrant is trisected by the lines L1L_{1} and L2L_{2} passing through the origin. The tangent of an angle between the lines L1L_{1} and L2L_{2} is:

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