(a)

The equation of tractrix is .

Differentiate on each side with respect to .

Derivative of the hyperbolic secant function: .

.

(b)

The equation of tractrix is , .

From (a):

.

Slope of the tangent is derivative of the function at the given point.

Let the point  is .

.

Slope of the tangent line is .

Point-slope form of line equation is .

Substitute  and  in the above equation.

The tangent line is .

The tangent line intersects the -axis at point  .

Substitute  in .

.

The distance between   and   is .

Substitute .

.

The distance between  and  is .

(a) .

(b) The distance between  and  is .