How would I graph the parametric curve defined by:?

Question

x=6cost, y=3sint, 0≤ t≤ 2pi

Any help would be appreciated. I know you can't necessarily graph but explanations would help. Please explain as thoroughly as possible so that I can learn the concept and complete similar problesm on my own. Thank you so much and 10 points to the best answer!

Answer 1

x = 6 cos(t)

y = 3 sin(t)

Therefore:

(x / 6)^2 + (y / 3)^2 = 1

x^2 / 36 + y^2 / 9 = 1.

That's an ellipse centred at (0, 0) with a horizontal major axis ending at (- 6, 0) and (6, 0), and vertical minor axis ending at (0, - 3) and (0, 3).

Going back to the parametric equation, pick a few first quadrant values for t, evaluate (x, y) and plot the point. The upper right quadrant can then be mirrored in both axes to complete the ellipse.