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

Solution

(x-4)²+y²=16

The relationship between rectangular coordinates and polar coordinates are

x²+ y²=R² and x=R cos theta y= Rsin theta

(x-4)²+ y²=16

x²+16-8y+y²=16

x²+y²-8y=0

R²-8Rcos theta=0

R(R-8cos theta)=0

R-8cos theta=0

R=8cos theta