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Math Help - Curve in the plane

  1. #1
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    Curve in the plane

    Hello,

    I want to determine an equation for this curve, but i doesn't know how it look like:

    -The curve is in the plane and only in one quadrant (i.e. in this part of the plane
    {(x,y): x,y>0}
    -at any point a of the curve there is a tangent line, s.t. this line intercects the positive y-axis in b and |a-b|=1.

    Is this curve really unique? And how does it look like?
    How can i grasp this curve as a equation?

    up to now, i look for a parametrization of the curve because it is characterized with the tangent vector at any point.
    So we have:
    c(t)=(c_1(t),c_2(t)) \subset {(x,y): x,y>0} and |a-b|=1
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  2. #2
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    Opalg's Avatar
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    This curve is called a tractrix. You may get some ideas here.
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