Question

In problem 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.

$x=t+2,y=\sqrt{t};t\ge 0$

Short answer

The answer is$y=\sqrt{x-2}.$

Step-by-step solution

Step 1. Given information.

$x=t+2,y=\sqrt{t};\text{and}t\ge 0$is given.

Step 2. Calculation.

Graph the curve defined by the parametric equations -

$x=t+2,y=\sqrt{t};t\ge 0$

$t$	$x$	$y$	$(x,y)$
$0$	$2$	$0$	$(2,0)$
$1$	$3$	$1$	$(3,1)$
$2$	$4$	$\sqrt{2}$	$(4,\sqrt{2})$
$3$	$5$	$\sqrt{3}$	$(5,\sqrt{3})$

We find the rectangular equation by eliminating the parameter t from the parametric equations.

$$\begin{gathered} y=\sqrt{t} \\ {y}^2=t \end{gathered}$$

Put the value of t in the equation -

role="math" localid="1648227471219" $$\begin{gathered} x=t+2 \\ x=y^2+2 \\ {y}^2=x-2 \\ y=\sqrt{x-2} \end{gathered}$$

Thus, the equation is$y=\sqrt{x-2}.$