Consider the following. x = et − 5, y = e2t (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

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

i think c. but don't trust it.

step-by-step explanation:

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation: