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Chapter 6: Problem 35

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

Short Answer

Expert verified
The graph of the parametric equations is a parabola that opens upwards. It's not connected to a specific point because the 't' parameter is allowed to vary over the entire set of real numbers.

Step by step solution

01

Understand the Parametric Equations

The given parametric equations are \(x = t\) and \(y = t^{2}\). So, for any value of 't', the corresponding 'x' value would be 't' and the 'y' value would be the square of 't'.
02

Create a table of values

Create a table of values for 't', 'x', and 'y'. Choose a range of values for 't'. Since no range is specified in the problem, you might take 't' from -3 to 3 for instance. Compute the corresponding 'x' and 'y' for these values of 't'.
03

Plot the points

Using a graphing utility or graph paper, plot each (x, y) point that the table produced.
04

Draw the Curve

Draw the curve that passes through the plotted points. The curve should be smooth and continuous because 't' can be any real number in these parametric equations.

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Most popular questions from this chapter

Convert the polar equation $$r=2(h \cos \theta+k \sin \theta)$$ to rectangular form and verify that it is the equation of a circle. Find the radius of the circle and the rectangular coordinates of the center of the circle.

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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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In Exercises \(91-116\), convert the polar equation to rectangular form. $$r=\frac{1}{1-\cos \theta}$$
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