rewrite the given equation using the substitutions x=r cos theta and y=r sin theta. Simplify your answer. x^2+y^2+3x=0

Answer 1

so, what's the trouble? Just plug and chug.
x^2+y^2 = r^2, so
r^2+3rcosθ = 0
r(r+3cosθ) = 0

If you want just r=f(θ) then you have to solve for r using the quadratic formula.