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Math Help - The length of AB

  1. #1
    leo
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    Arrow The length of AB

    Hello, can someone help me answer this question? Thanks in advance

    Points A and B are on the curve y= (4x^2)+7x-1, and (0,0) is the midpoint of the line segment AB. Find the length of AB.
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  2. #2
    Senior Member nikhil's Avatar
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    y=4x^2+7x-1
    let coordinates of A be (x1,y1)
    coordinates of B be (x2,y2)
    since (0,0) is the midpoint of line segment AB therfor
    (x1+x2)/2=0
    x1=-x2
    similarly y1=-y2

    now according to the equation
    y1^2=4(x1)^2+7x1-1 and
    y2^2=4(x2)^2+7x2-1
    since y1=-y2 therefor
    4(x1)^2+7x1-1 +4(x2)^2+7x2-1 =0
    now after putting x1=-x2 we get
    8(x2)^2=2 therefor
    x2=+-(1/2)
    let x2=(1/2) so x1=(-1/2)
    put these value in equation and obtain value of y1 and y2
    so A=(-1/2,-7/2) and B=(1/2,7/2)
    using distance formula we get distance between them=sqrt[50]
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