Eliminate the parameter????

Question

Eliminate the parameter 

 x=4+2 cos∅

  y=1+2 sin∅

I think i can solve it like this but i am not sure

x=4+2cos∅

x-2=4cos∅

x-2/4=cos∅

 

Answer 1

 X = 4 + 2 Cos θ

 Y  = 1 + 2 Sin θ

 

    (X- 4 ) /2 = Cos θ

    ( Y -1 )/ 2 = Sin θ

 

  ( X-4 ) ^ 2   +  ( Y - 1 ) ^2 = Cos ^2 θ + Sin ^2 θ

        4                   4 

 

   ( X - 4 ) ^2 + ( Y -1 ) ^2 = 4

 

  Equation of a circle centered @ ( 4 , 1 ) with radius 2