WILL MARK BRAINLIEST
Consider the parametric equations below.

x = t2 − 2, y = t + 1, −3 ≤ t ≤ 3

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.

(b) Eliminate the parameter to find a Cartesian equation of the curve. for −2 ≤ y ≤ 4

(a) In attachment

(b) x = y² - 2y - 1,    −2 ≤ y ≤ 4

Step-by-step explanation:

(a)

The graph of the given parametric equation is given in the attachment.

The direction in which the curve is traced as t increases, is indicated by black arrows.

(b)

To eleminate the parameter t, we simultaneously solve both the equations.

So, we have the equations:

x = t² - 2   ----- equation (1)

y = t + 1   ----- equation (2)

So, from equation (2), we have:

t = y - 1

Substituting this in equation (1), we get:

x = (y - 1)² - 2

x = y² - 2y + 1 - 2

x = y² - 2y - 1

Now, for limits of y, we use equation (2)

For initial limit, t = -3

y = - 3 + 1 = - 2

For final limit, t = 3

y = 3 + 1 = 4

Therefore, the final relation after eliminating t is:

x = y² - 2y - 1,    −2 ≤ y ≤ 4

24 units

step-by-step explanation: