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.

$x=t^2,y=Int;t>0.$

Short answer

The equation is$y=\frac{1}{2}Inx.$

Step-by-step solution

Step 1. Given information.

$x=t^2,y=Int$is given.

Step 2. Form the graph and equation.

we form the rectangular equation by eliminating t in the equation-

$$\begin{gathered} t>0 \\ x=t^2 \\ \sqrt{x}=\sqrt{t^2} \\ t=\sqrt{x} \end{gathered}$$

Put the value of t-

$$\begin{gathered} y=Int \\ y=In{x}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \\ y=\frac{1}{2}Inx \end{gathered}$$

Thus, the equation is $y=\frac{1}{2}Inx.$

Graph the curve defined by the parametric equations -

$t$	$x$	$y$	$(x,y)$
$1$	$1$	$0$	$(1,0)$
$2$	$4$	$In2$	$(4,In2)$