I really need help with converting rectangular equations to polar!!! URGENT

Question

 

Set B: Rectangular to Polar: Convert these equations to polar format

2. (x–2)² + y² = 4

3. (x–4)² + (y–3)² = 25

Answer 1

(x–2)² + y² = 4

 

Now, We  use the formulas giving the relationship between polar and rectangular coordinates:

 

R ² = x ² + y ²,

y = R sin t

x = R cos t

 

x²-4x+4+y²=4

 

x²+y²-4x+4-4=0

 

x²+y²-4x=0

 

R²-4 Rcost=0  ----------------used (R²=x²+y²) and x=Rcost

R(R-4cost)=0

 

R=0

 

or

 

R-4cost=0

R=4cost   .......polar form of equation

 

The equation R = 0 is the pole. But the pole is included in the graph of the second equation  R = 4 cos t