Answer:
D. (-x+5)^2/9+(y-4)^2/4=1 (I assume there was a mistype)
Step-by-step explanation:
The first step is isolating the sine and cosine functions.
x=5-3cos(t)
x + 3cos(t) = 5
3cos(t) = 5 - x
cos(t) = (5 - x)/3
y=4+2sin(t)
y - 4 = 2sin(t)
(y - 4)/2 = sin(t)
Then, square at both sides of the equal sign
cos²(t) = (5 - x)²/3² = (5 - x)²/9
sin²(t) = (y - 4)²/2² = (y - 4)²/4
Recall the trigonometric identity and replace.
cos²(t) + sin²(t) = 1
(5 - x)²/9 + (y - 4)²/4 = 1
