Plane Curves(Continuation of Exercise 7. )a. Use the

Chapter 13, Problem 8E

(choose chapter or problem)

Problem        8E

Plane Curves

(Continuation of Exercise 7. )

a. Use the method of Exercise 7 to find N for the curve

b. Calculate N for directly from T using Equation (4) for the curve in part (a). Does N exist at t = 0? Graph the curve and explain what is happening to N as t passes from negative to positive values.

Reference: Exercise 7

Normals to plane curves

a. Show that   are both normal to the curve at the point (ƒ(t), g(t)).

To obtain N for a particular plane curve, we can choose the one of n or – n from part (a) that points toward the concave side of the curve, and make it into a unit vector. (See Figure 13.19.) Apply this method to find N for the following curves.