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
Practise AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane with exam-style questions for A Level Maths. 110 questions covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
