Question

Janet is drawing the path formed by the parametric equations x=2+3 sin t and y=1-1/2cos t. Which curve did she draw??

Answer 1

Sin²t +cos²t =1

 x=2+3 sin t
sin t=(x-2)/3

y=1-1/2cos t
y-1= - (cos t)/2 
cos t =-(y-1)/(1/2)

(x-2)²/3² + (y-1)²/(1/2)² = 1
Ellipse