Answer:
The Cartesian equation is
y = x² + 10x + 25
Step-by-step explanation:
Given the parametric equations:
x = e^t - 5
y = e^(2t)
We are required to obtain the Cartesian equation by eliminate the parameter 't'. To do this, let us rewrite the equation y = e^(2t) by taking square roots of both sides as
√y = e^t.
This can be easily subtracted from x = e^t - 5
Subtracting, we have
x - √y = e^t - 5 - e^t
x - √y = -5
√y = x + 5
Squaring both sides, we have
y = (x + 5)²
y = x² + 10x + 25.
And this is the Cartesian equation of the curve.
THE GRAPH IS SHOWN IN THE ATTACHMENT.
It is plotted for -5 ≤ t ≤ 5
