# Thread: Eliminate the parameter to find a Cartesian equation

1. ## Eliminate the parameter to find a Cartesian equation

Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!

Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.

x(t)= 6ln(5t) , y(t)= √t

Thanks!

2. Hello Inexcess

Welcome to Math Help Forum!
Originally Posted by Inexcess
Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!

Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.

x(t)= 6ln(5t) , y(t)= √t

Thanks!
You have:

$\displaystyle x = 6\ln (5t)$

$\displaystyle \Rightarrow \ln(5t) = \frac{x}{6}$

$\displaystyle \Rightarrow 5t = e^{\frac{x}{6}}$

$\displaystyle \Rightarrow t = \tfrac15e^{\frac{x}{6}}$

$\displaystyle \Rightarrow \sqrt{t} = \sqrt{\tfrac15e^{\frac{x}{6}}}$

which can be written as

$\displaystyle \sqrt{t}= \tfrac{1}{\sqrt5}e^{\frac{x}{12}}$

But $\displaystyle y = \sqrt{t}$

So a Cartesian equation is

$\displaystyle y =\tfrac{1}{\sqrt5}e^{\frac{x}{12}}$