what is the rectangular form of: r= cos (theta) - 1

Question

I got x=x^2+y^2+\sqrt{x^2+y^2} but when I graphed on desmos it didn't give me a graph like the original equation

Answer 1

convert r=cosθ-1 to rectangular form

polar coordinates are x=rcosθ and y=rsinθ

x²+y²=r² is the equation of a circle with the center at the origin

r=√(x²+y²)

r=cosθ-1

multiply both sides by r

r*r=r*(cosθ-1)

r²=rcosθ-r

substitute for r², r, and rcosθ

(x²+y²)=x-√(x²+y²)