Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. $x = t$
$y = \ln t$
A) $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $y = e ^ { x }$
C) $y = x ^ { 2 } - 1 , x \geq 0$
D) $y = \ln x$
E) $y = x + 1$

Question

Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. $x = t$
$y = \ln t$
A) $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B) $y = e ^ { x }$ 
C) $y = x ^ { 2 } - 1 , x \geq 0$ 
D) $y = \ln x$ 
E) $y = x + 1$

Quizplus · Accepted Answer

Eliminating the parameter $t$ from the given parametric equations, we get $x = t$ and $y = \ln t$. Solving for $t$ in $x = t$, we get $t = x$. Substituting this into $y = \ln t$, we get $y = \ln x$. Thus, the rectangular equation is $y = \ln x$. Sketching the curve, we see that it is the graph of the natural logarithm function.

Sketch the Curve Represented by the Parametric Equations, and Write x=tx = tx=t

Sketch the Curve Represented by the Parametric Equations, and Write $x = t$