Which equation in rectangular form describes the parametric equations x=5-3cost and y=4+2sint?

A. (x+5) ^2/9 + (y+4) ^2/4=1

B. (y+4) ^2/2 - (x+5) ^2/3=1

C. (y-4) ^2/2 - (x-5) ^2/3=1

D. (x-5) ^2/9 + (y-4) ^2/4=1

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