x=4 cost, y= 2 sint on the interval

Question

0 ≤ t ≤ 2π

what is the Cartesian equation? nd describe the graph giving the (x,y) co-ordinates ... stating the initial point and the terminal point. ?

i found the cartesian equation as

y= square root of 4-x^2/4

plz help .. i know it a complete circle but i cant have "y" as negative .. so ...

Answer 1

cos t = x/4 and sin t = y/2
we know that sin^2 t + cos^2 t = 1

x^2/16 + y^2/4 = 1
times 16
x^2 + 4y^2 = 16

this is NOT a circle, but rather an ellipse
I hope you know the properties of this ellipse
a = 4, b=2

vertices along the x-axis are (-4,0) and (4,0)
along the y-axis they are (0,2) and (0,-2)

Answer 2

what i did is i found the cartesian equation as x=2 sqrt of 4-y^2 nd then i took the table of value nd chose numbers nd substituded but the problem is that in my cartesian equation "x" can not be negative so i only found y-axis as (0,2) and (0,-2) and x-axis as (4,0) so hw can fix this where did i go wrong? did u like find the coordinates from its properties (a = 4, b=2)?