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Minimum area of the triangle cut off from the axes by a line through a fixed point

This type of question, asked 2 times: 19 Apr 2026 S1, 13 May 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    19 Apr 2026 S1

    57
    A straight line L passes through the point of intersection of the lines x−y+1=0x - y + 1 = 0 and 2x+y−7=02x + y - 7 = 0. If L intersects the positive x-axis at A(a,0)A(a, 0) and the positive y-axis at B(0,b)B(0, b), then the minimum area of the triangle OABOAB (where OO is the origin) is ....

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  2. Question 2

    13 May 2026 S1

    58
    A straight line passes through the point (3,3)(3, 3) and intersects the positive xx and yy axes at the points A(h,0)A(h, 0) and B(0,k)B(0, k) respectively. If O is the origin, then the minimum area of △OAB\triangle OAB is:

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