Answer
(a) $r=4(cos~θ+sin~θ)$
(b) See graph below
Work Step by Step
(a)
$x=r~cos~θ$
$y=r~sin~θ$
$x^2+y^2=r^2$
$x^2+y^2=4x+4y$
$r^2=4r~cos~θ+4r~sin~θ$
$r[r-4(cos~θ+sin~θ)=0~~$ Since $r\ne0$:
$r-4(cos~θ+sin~θ)=0$
$r=4(cos~θ+sin~θ)$
(b) Use:
$r=4(cos~θ+sin~θ)$
