Find an equation of y as a function of x for the parametric equations given below by eliminating the parameter. Also, indicate the direction of the curve.x = e²^t, y = t, t ? 0 A) $y = \frac { 1 } { 2 } \ln x , \quad x \geq 1 \text {, right to left }$ B) $y = \frac { 1 } { 2 } \ln x , \quad x \geq 1 \text {, left to right }$ C) $y = 2 \ln x , \quad x \geq 1 , \quad \text { right to left }$ D) $y = 2 \ln x , \quad x \geq 1 , \quad \text { left to right }$

Question

Quizplus · Accepted Answer

Given $x = e^{2t}$ and $y = t$, solving for $t$ in terms of $x$ gives $t = \frac{1}{2}\ln(x)$, thus $y = \frac{1}{2}\ln(x)$, with $x \geq 1$ because $e^{2t}$ is always positive and increases as $t$ increases, indicating a left to right direction.

Find an Equation of Y as a Function of X y=12ln⁡x,x≥1, right to left y = \frac { 1 } { 2 } \ln x , \quad x \geq 1 \text {, right to left }y=21​lnx,x≥1, right to left

Find an Equation of Y as a Function of X $y = \frac { 1 } { 2 } \ln x , \quad x \geq 1 \text {, right to left }$