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Math Help - Find coordinates of fixed point if...?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find coordinates of fixed point if...?

    The straight lines x(a+2b) + y(a + 3b) = a + b for different values of a & b pass through a fixed point whose coordinates are :

    A)(1,-2)
    B)(2, -1)
    C)(1, 2)
    D)None

    Only one option is correct.

    It seems that the question is actually an inverted form of finding the locus of the fixed point for some condition. I am unable to make any headway.
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  2. #2
    Member Henderson's Avatar
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    If you plug in point B, you get:

    2(a+2b)-1(a+3b)=a+b
    2a+4b-a-3b=a+b
    a+b=a+b

    Therefore, point B will be on any version of this line, regardless of what a&b actually are.
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