Question

A plane curve is defined by the following paramedic equation:

x=2cos(t)
y=sin(t)

which of the following statements best describes the curve?

A) the parameter is x and the curve contains the points y=sin(t)
B) the parameter is y and the cube contains the points x=2cos(t)
C) the parameter is t and the curve contains the set of points (2cos(t),sin(t))
D the parameter is t and the curve contains the points (sin(t),2cos(t))

Answer 1

1. The parameter is t and the curve contains the set of points

2. Up to the left and then up to the right

Looks at the graph to find this answer to be true

3. (-3,-1)

x=2t-1

y=t^2

Plug in t=-1 in every t and find this answer to be true

Answer 2

x = 2 cos t and y = sin t \\ For the given parametric equations the common between them is t \\ So. The parameter is t. \\ The general coordinates for the points of the curve will be (x,y) \\ So, the coordinates will be ( 2 cos t , sin t )
The correct answer is option C
C) the parameter is t and the curve contains the set of points (2cos(t),sin(t))