Question

Precalc help?!

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

Answer 1

The answer is `option (B)`

Explanation:

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`

Completing the square

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

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

The answer is `option (B)`