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Geometry

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What is the equation of a line through (-2,5) and whose segment intercepted between the axes in the 2nd quadrant is 7sqrt2?


Please help me solve this

  • Geometry - ,

    Where are you getting these ?

    let P be (-2,5)
    let the x-intercept be A(x,0) and the y-intercept be B(0,y)

    so first of all:
    x^2 + y^2 = (7√2)^2 = 98

    now the slope of AP = slop BP
    (y-5)/(2 = -5/(x+2)
    cross-multiplying and re-arranging I got
    xy + 2y = 5x
    y(x+2) = 5x
    y = 5x/(x+2)

    sub that into above:
    x^2 + y^2 = 98
    x^2 + 25x^2/(x+2)^2 = 98
    x^2(x+2)^2 + 25x^2 = 98(x+2)^2
    expanding all this and simplifying I got the horrible equation

    x^4 + 4x^3 - 69x^2 - 392x - 392 = 0
    at this point I "cheated" and ran it through Wolfgram
    http://www.wolframalpha.com/input/?i=x%5E4+%2B+4x%5E3+-+69x%5E2+-+392x+-+392+%3D+0
    to get an exact value of x = -7

    so y = -35/(-5) = 7
    we can now find the slope of our line which is
    (5-0)/(-2+7) = 1, wow!

    equation is

    y = x + 7

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