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Variable line through a fixed point meeting the axes: minimise OA + OB or the area OAB

This type of question, asked 3 times: 31 Jan 2024, 6 Apr 2024, 9 Apr 2024. All 3 questions below, oldest first.

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  1. Question 1

    31 Jan 2024

    154
    Let a variable line passing through the centre of the circle x2+y2−16x−4y=0x^{2}+y^{2}- 16x - 4y = 0, meet the positive co-ordinate axes at the point AA and BB. Then the minimum value of OA+OBOA + OB, where OO is the origin, is equal to

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  2. Question 2

    6 Apr 2024

    73
    Let a variable line of slope m>0m > 0 passing through the point (4,−9)(4, - 9) intersect the coordinate axes at the points AA and BB. the minimum value of the sum of the distances of AA and BB from the origin is

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  3. Question 3

    9 Apr 2024

    68
    A variable line LL passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points AA and BB. The minimum area of the triangle OABOAB, where OO is the origin, is:

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