We have an answer to "How do you write x=et−1 and y=e2t as..."

Slade Higgins

Answered question

2022-04-22

How do you write

x = e^{t} - 1 and y = e^{2} t

as a cartesian equation and then sketch the curve?

botassaiby

Beginner2022-04-23Added 16 answers

Step 1
First of all I think that, maybe, there is a little mistake in your writing.
Doesn't the function is:

x = e^{t} - 1

y = e^{2 t}

instead of yours?
Step 2
If I am right, than:

x + 1 = e^{t} \Rightarrow= \ln (x - 1)

and

y = e^{2 \ln (x + 1)} \Rightarrow y = e^{\ln ({(x + 1)}^{2})} \Rightarrow y = {(x + 1)}^{2}

(this is because:

e^{\ln f (x)} = f (x))

And this is the equation of a parabola centered in

V (- 1, 0)

and that passes from the points

(0, + 1)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?