Chapter 9.1, Problem 62E

To determine

(a)

To prove:

the tractrix equation function $y^2+{\left(\frac{y}{y^{\prime }}\right)}^2=l^2$ and also conclude that $y^{\prime }=-\frac{y}{\sqrt{l^2-y^2}}$.

Why choose the negative square root in tractrix equation.

To determine

(b)

To prove:

that tractrixis the graph of $x=\mathcal{l}\ln \left(\frac{\mathcal{l}+\sqrt{{\mathcal{l}}^2-y^2}}{y}\right)-\sqrt{{\mathcal{l}}^2-y^2}$.