QUICK HELP?!?!?!?!

Question

rewrite r=4costhea in rectangular form

show work. Your final answer must be in standard form of a circle.(x-h)^2+(y-k)2=r2

Answer 1

in terms of x,y

cos(angle)=x/√(x²+y²)

r=√(x²+y²)

now have

x²+y²=4x

completing square

(x-2)²+y²=2²

Answer 2

r = 4cosθ

r² = 4rcosθ <-- Multiply both sides by r to use the substitution x=rcosθ on the right-hand side

x²+y² = 4x <-- Recall that r²=x²+y²

x²-4x+y² = 0

x²-4x+4+y² = 0+4 <-- Completing the Square

(x-2)²+y² = 4

Hope this helped!