Question

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility

$x=t+2,y=1t;t\ge 0$

Short answer

Rectangular equation of the given curve is

orientation and the graph are plotted in the solution

Step-by-step solution

Step. 1 Description

Given parametric equation

$x=t+2,y=1t;t\ge 0$

To find

a. Rectangular equation of the curve

b. Graph the curve, show its orientation and varify it by graphing utility

Step. 2 Simplification

$$\begin{gathered} x=t+2 \\ t=x-2eqn1 \\ y=\sqrt{t} \\ putthevalueoftfromequation1 \\ y=\sqrt{x-2};\{x-2\ge 0\} \end{gathered}$$

This is the rectangular form of the given curve

Step. 3 Simplification

Graph of the given parametric equation is plotted as

Step. 4 Simplification

The graph of the rectangular equation is plotted as

Both the equations represent the same graph and orientation. Hence it is varified.