This curve is called a tractrix. You may get some ideas here.
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: