Precalc help?!

Question

Find a rectangular equation for the curve r = 4cosθ

Answer choices:
A) (x-2)^2 +y^2 =4
B) (x+2)^2 + y^2 = 4
C) x^2 + (y+2)^2 = 4

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Answer 1 · 2018-07-21T05:55:55

The answer is #option (B)#

To transform from polar coordinates #(r,theta)# to rectangular corrdinates #(x,y)#, apply the following

#{(x=rcostheta),(y=rsintheta),(r^2=x^2+y^2):}#

Here,

The equation is

#r=4costheta#

#=>#

#r=4x/r#

#r^2=4x#

#x^2+y^2=4x#

#x^2-4x+y^2=0#

#x^2-4x+4+y^2=4#

#(x+4)^2+y^2=4#

The answer is #option (B)#