Draw a graph of the plane curve defined by the following parametric equations with the help of point plotting. Indicate the direction of the curve obtained corresponding to increasing values of t using arrows.

x = t − 5, y = 3t + 2; −1 ≤ t ≤ 4

Determine the coordinates of the point on the plane curve represented by the following parametric equations for the specified value of u.

x = u³ + 3, y = 7 − u⁴; u = 4

Obtain two distinct sets of parametric equations corresponding to the following equation.

y = 9x - 5

Plot the given polar coordinates on a polar coordinate system. 

(20, 5π/4)

Which of the following polar coordinates represents the same location as (-10, -π/6)?

I. (10, 17π/6)

II. (-10, 15π/6)

III. (10, 13π/6)

IV. (-10, 11π/6)

Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:

(21, -7√3)

Test the polar equation for symmetry and sketch its graph:

r = 5 + 11 cos θ