Convert the equation given below in rectangular coordinates

Convert the equation given below in rectangular coordinates into an equation in polar coordinates: (x 4)^2 + y^2= 16

(x-4)^2 + y^2=16

The relationship between polar and rectangular coordinates is

R^2=x^2 + y^2 and x=Rcos theta ,y=R sin theta

And we have

(x-4)^2 + y^2=16

x^2 + 16 -8x +y^2=16

x^2-8x+y^2=0

R^2 - 8R cos theta=0

R(R- 8cos theta)=0

R-cos 8theta=0

R=8cos theta