Which equation in rectangular form describes the parametric equations x=5-3cos(t) and y=4+2sin(t)

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

1 answer

We can see that the parametric equations x=5-3cos(t) and y=4+2sin(t) are equivalent to the equations x=3cos(t)+5 and y=2sin(t)+4.

To convert these parametric equations to rectangular form, we can use the identities cos^2(t) + sin^2(t) = 1. Squaring and adding the two equations, we get:

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

Therefore, the correct equation in rectangular form is:

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