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Chapter 6: Problem 38

Use a graphing utility to graph the curve represented by the parametric equations. $$\begin{aligned} &x=t+1\\\ &y=\sqrt{2-t} \end{aligned}$$

Short Answer

Expert verified
Once the parametric equations are inputted into a graphing utility, they will provide an accurate representation of the curve on the x-y plane. The specific shape of the curve will depend on the graphing utility and the chosen range for the parameter \(t\).

Step by step solution

01

Understanding the Parametric Equations

In this exercise, we are given two parametric equations \(x = t + 1\) and \(y = \sqrt{2 - t}\). Here, \(t\) is the parameter that independently determines the values for \(x\) and \(y\). Parametric equations like these help in describing a curve in the x-y plane.
02

Inputting the Equations into the Graphing Utility

Next, you need to input the parametric equations into a graphing utility. Most graphing utilities have an option for plotting parametric equations. Place the expression \(t + 1\) for \(x\) and the expression \(\sqrt{2 - t}\) for \(y\). The parameter \(t\) is generally varied from a minimum to a maximum value. To accurately plot this curve, use a reasonable range for \(t\), for instance from \(t = -1\) to \(t = 2\).
03

Interpreting the Resulting Curve

Having input the equations and the range for \(t\), you will see a curve plotted on the x-y plane. The resultant curve represents all the possible (x, y) coordinates obtained from the given parametric equations.

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Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. If the vertex and focus of a parabola are on a horizontal line, then the directrix of the parabola is vertical.

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