Chapter 1, Problem 13RCC

(a)

To determine

To find: The definition of the given term.

Answer to Problem 13RCC

The parametric curve is defined.

Explanation of Solution

Given:

The given term is parametric curve.

Calculation:

Consider the functions for $t$ are $x$ and $y$ , where $t$ is the parameter and the parametric equation are $x=f\left(t\right)$ and $y=g\left(t\right)$ .

For every value of $t$ there is a point $\left(x,y\right)$ , this points can be plotted on the coordinate plane and as the value of $t$ changes the value of the points also changes from the curve $C$ known as the parametric curve.

(b)

To determine

To find: The way in which the parametric curve is obtained.

Answer to Problem 13RCC

The parametric curve is obtained by joining the parametric points.

Explanation of Solution

The value of the parameter $t$ is changed to obtain the points $\left(x,y\right)$ that are plotted on the parametric curve. When all the points are joined the parametric curve is obtained.

(c)

To determine

To find: The way in which the parametric curve is more useful than the curve of the form $y=f\left(x\right)$ .

Answer to Problem 13RCC

The parametric curve is more important as it gives useful points to plot on the coordinate plane.

Explanation of Solution

The parametric curve is more important than the curve obtained by the function of the form $y=f\left(x\right)$ because the parameter curve have different points $\left(x,y\right)$ on the curve that are obtained by varying the parameter $t$ .