# Curve in the plane

• November 23rd 2010, 09:12 PM
Sogan
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:
$c(t)=(c_1(t),c_2(t)) \subset {(x,y): x,y>0} and |a-b|=1$
• November 24th 2010, 03:49 AM
Opalg
This curve is called a tractrix. You may get some ideas here.