Eliminate the parameter to find a Cartesian equation

**Inexcess** · August 31st 2009, 12:00 PM

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!

**Grandad** · August 31st 2009, 12:34 PM

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:

$x = 6\ln (5t)$

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

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

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

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

which can be written as

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

But $y = \sqrt{t}$

So a Cartesian equation is

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

Grandad

**Inexcess** · August 31st 2009, 12:47 PM

Thank you! I greatly appreciate it.

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