15–30. Working with parametric equations Consider the following parametric equations.

a. Eliminate the parameter to obtain an equation in x and y.

b. Describe the curve and indicate the positive orientation.

x = cos t, y = 1 + sin t; 0 ≤ t ≤ 2π

15–30. Working with parametric equations Consider the following parametric equations.

a. Eliminate the parameter to obtain an equation in x and y.

b. Describe the curve and indicate the positive orientation.

x = r − 1, y = r³; −4 ≤ r ≤ 4

15–30. Working with parametric equations Consider the following parametric equations.

a. Eliminate the parameter to obtain an equation in x and y.

b. Describe the curve and indicate the positive orientation.

x = 8 + 2t, y = 1; −∞ < t < ∞

31–36. Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in x and y.

x=2 sin 8t, y=2 cos 8t 

31–36. Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in x and y.

x=tan t, y=sec ² t−1 

11–14. Working with parametric equations Consider the following parametric equations.

c. Eliminate the parameter to obtain an equation in x and y.

d. Describe the curve.

x=2 t,y=3t−4;−10≤t≤10 

11–14. Working with parametric equations Consider the following parametric equations.

c. Eliminate the parameter to obtain an equation in x and y.

d. Describe the curve.

x=−t+6, y=3t−3; −5≤t≤5 

37–52. Curves to parametric equations Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique.

A circle centered at the origin with radius 4, generated counterclockwise