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Math Help - Intersection of 2 curves at right angles

  1. #1
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    Intersection of 2 curves at right angles

    Hey guys, I have a question that I am stuck atm and need some help with.

    "For what values of the nonzero constant k do the curves y=kx^2 and y=k(x-2)^2 intersect at right angles?"

    I started off by finding the intersection point of the 2 curves:
    kx^2 = k(x-2)^2
    x = 2

    After which I differentiate to find my gradient or slope:
    For the curve y = kx^2, m1 = 2kx
    For the curve y = k(x-2)^2, m2 = 2k(x-2)

    I understand that since the 2 curves intersect at 90 degrees, m1.m2 = -1

    But when i sub x=2 into my m2, i get 0 which gives me m1.0 = -1


    I am definitely wrong somewhere but I cannot really figure it out. Am I even on the right track to solving this question?

    Cheers,
    Dickson
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  2. #2
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    Assuming k is nonzero...

    kx^2=k(x-2)^2
    iff
    kx^2-k(x-2)^2=0
    factor
    k(x^2-(x-2)^2)=0
    iff
    x^2-(x-2)^2=0, since k is non zero.

    iff x^2-(x^2-4x+4)=0
    x^2-x^2+4x-4=0
    4x=4
    x=1, not 2.
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  3. #3
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    yea its x = 1!

    omg lol simple factorization mistake

    thx anyway,
    Dickson
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