Chapter 8, Problem 8RCC

(a)

To determine

To sketch: the curve of the given parametric equations

Answer to Problem 8RCC

The procedure to sketch the curve of the parametric equations is explained.

Explanation of Solution

Given: $x=f\left(t\right),y=g\left(t\right)$

Calculation:

The procedure to sketch the curve of the parametric equations $x=f\left(t\right),y=g\left(t\right)$

If f and g are functions defined on an interval I , then the set of points $\left(f\left(t\right),8\left(t\right)\right)$ is a plane curve.

For different value of t, get a point on the curve and then write these values in a table.

For example, if $t=0$ , then $x=f\left(t\right)=f\left(0\right)$ and $y=g\left(t\right)=g\left(0\right)$ .

So the corresponding point is $\left(f\left(0\right),g\left(0\right)\right)$ .

Then, plot the points $\left(x,y\right)$ determined by the values of t in a table.

Conclusion:

Therefore, the procedure to sketch the curve of the parametric equations is explained.

(b)

To determine

To explain: eliminate the parameter.

Answer to Problem 8RCC

The parameter is eliminated.

Explanation of Solution

Calculation:

The method to eliminate the parameter:

The curve given by parametric equations can be represented by a single rectangular equation in x and y .

The process of finding this equation is called eliminating the parameter.

Solve for parameter in one equation, and then substitute its value into the other equation.

Thus, the parameter is eliminated.

Conclusion:

Therefore, the parameter is eliminated.