Question

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

Answer 1

D. (-x+5)^2/9+(y-4)^2/4=1 (I assume there was a mistype)

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