A precision industrial laser traces a path C C\,C defined by the parametric equations
x=5−3sin(t)andy=4+2cos(t) x = 5 - 3\sin(t) \quad \text{and} \quad y = 4 + 2\cos(t) x=5−3sin(t)andy=4+2cos(t)where 0≤t<2π0 \le t < 2\pi0≤t<2π, and x,y x, y\,x,y are distances in millimetres. Which of the options shown below is a Cartesian equation for the path CCC?
(x−5)29+(y−4)24=1\frac{(x-5)^2}{9} + \frac{(y-4)^2}{4} = 19(x−5)2+4(y−4)2=1
(x+5)29+(y+4)24=1\frac{(x+5)^2}{9} + \frac{(y+4)^2}{4} = 19(x+5)2+4(y+4)2=1
(x−5)2+(y−4)2=13(x-5)^2 + (y-4)^2 = 13(x−5)2+(y−4)2=13
(x−5)23+(y−4)22=1\frac{(x-5)^2}{3} + \frac{(y-4)^2}{2} = 13(x−5)2+2(y−4)2=1
