How do you write x=e^{t}-1\ \text{and}\ y=e^{2}t as a cartesian

Slade Higgins

Slade Higgins

Answered question

2022-04-22

How do you write x=et1 and y=e2t as a cartesian equation and then sketch the curve?

Answer & Explanation

botassaiby

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=et1
y=e2t instead of yours?
Step 2
If I am right, than:
x+1=et⇒=ln(x1) and
y=e2ln(x+1)y=eln((x+1)2)y=(x+1)2
(this is because: elnf(x)=f(x))
And this is the equation of a parabola centered in V(1,0) and that passes from the points (0,+1).

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