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A straight line x/a -y/b =1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of coordinates .find the equation of straight line

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3 answers

  1. since (8,6) lies on it,
    8/a - 6/b = 1
    (8b - 6a)/(ab) = 1
    8b - 6a = ab
    8b - ab = 6a
    b(8 - a) = 6a
    b = 6a/(8-a) **

    x/a - y/b = 1 is in the intercept form, that is
    the x-intercept is (a,0)
    the y-intercept is (0,b)
    so the area of the triangle is (1/2)(ab)
    (1/2)(ab) = 12
    ab = 24 ***

    sub ** into ***
    a(6a)/(8-a) = 24
    6a^2 = 192 - 24a
    a^2 + 4a - 32 = 0
    (a+8)(a-4) = 0
    a = -8 or a = 4

    if a = 4, b = 6
    x/4 - y/6 = 1 ---> 6x - 4y = 24 or 3x - 2y = 12

    if a = -8, b = -3
    x/-8 - y/-3 = 1 ---> -3x + 8y = 24 or 3x - 8y = -24

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  2. Very useful

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  3. Ty

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