Question

Match the parametric curve to its description. Be careful: It is possible that the same description fits more than one parametric curve!


(a) (t + 1,4t−2)
(b) (t^2,3t^2)
(c) (cost,2(cost)^2 + cost)
(d) ((2t + 1)sint,(2t + 1)cost)
(e) (2t−1,5)


(1) A portion of a parabola.
(2) A straight line traversed at constant speed.
(3) A straight line traversed at variable speed.
(4) A circle.
(5) Doesn’t match any other description.

Answer 1

Well, I suppose if you do not see it as is, you can do x and y

for example in (a)
y = 4t-2
x = t+1
so
t = x-1
y=4(x-2) - 2
y = 4 x -10
dx/dt=dy/dt = 0 so constant speed

(d) If you do no see it is a circle, do the same thing again
y = (2t+1) cos t
y^2 = (2t+1)^2 cos^2 t
x^2 = (2t+1)^2 sin^2 t

x^2 + y^2 = (2t+1)^2
circle of expanding radius

Answer 2

I used a graphing site for parametric curve and (d) gives me a graph like a roller coaster. so it is a circle ?how about for b and e??

Answer 3

LOL e is a horizontal line, y = 5

b is a parabola, do what I suggested.

Answer 4

so what description(1-5)fits the given parametric curves(a-b)? cheers.