How do you graph the polar equation #r^2=9sin2theta#? Trigonometry The Polar System Graphing Basic Polar Equations 1 Answer Salvatore I. Nov 8, 2016 #(x^2+y^2)^2-18xy=0# Explanation: #x=rhocostheta# from which #costheta=x/rho# #y=rhosintheta# from which #sintheta=y/rho# #rho=root2(x^2+y^2)# #rho^2=x^2+y^2# #rho^2=18sinthetacostheta=# #rho^2=18(xy)/rho^2# #rho^4=18xy# #(x^2+y^2)^2=18xy# Answer link Related questions What are limacons and cardioids? How do you graph basic polar equations? How do you determine the shape of a limaçon from the polar equation? How do you graph #r = 1.5#? How do you graph #\theta = 30^\circ#? What does the graph of #r = \cos \theta# such that #0^\circ \le \theta \le 360^\circ# look like? What is the general form of limacons and cardioids and how do you graph transformations? How do you graph the equation #r = 1 + cos( theta )#? How do you graph #r=3-2costheta#? How do you graph #r=1-cosx#? See all questions in Graphing Basic Polar Equations Impact of this question 5393 views around the world You can reuse this answer Creative Commons License