Maths (Tangents and Normals)

find the values of p and q if slope of the tangent to the curve xy + pq + qy = 2(1, 1) is 2

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asked by Sykox

  1. xy' + y + qy' = 0
    y' = -y/(x+q)
    at (1,1) y' = -1/(1+q) = 2
    so, q = -3/2

    so, at (1,1)
    1 - 3/2 p - 3/2 = 2
    p = -5/3

    xy + 5/2 - 3y/2 = 2
    and the tangent line is
    y-1 = 2(x-1)


    visit wolframalpha.com and enter

    plot xy + 5/2 - 3y/2 = 2, y-1 = 2(x-1), x=0..2

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    posted by Steve

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