How do you convert #y= 3x^2-5x-y^2 # into a polar equation? Trigonometry The Polar System Converting Between Systems 1 Answer 1s2s2p Mar 20, 2018 #r=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)# Explanation: For this we need the following: #x=rcostheta# #y=rsintheta# #rsintheta=3(rcostheta)^2-5(rcostheta)-(rsintheta)^2# #rsintheta=3r^2cos^2theta-5rcostheta-r^2sin^2theta# #rsintheta+r^2sin^2theta=3r^2cos^2theta-5rcostheta# #sintheta+rsin^2theta=3rcos^2theta-5costheta# #rsin^2theta-3rcos^2theta=-sintheta-5costheta# #r=(-sintheta-5costheta)/(sin^2theta-3cos^2theta)=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)# Answer link Related questions How do you convert rectangular coordinates to polar coordinates? When is it easier to use the polar form of an equation or a rectangular form of an equation? How do you write #r = 4 \cos \theta # into rectangular form? What is the rectangular form of #r = 3 \csc \theta #? What is the polar form of # x^2 + y^2 = 2x#? How do you convert #r \sin^2 \theta =3 \cos \theta# into rectangular form? How do you convert from 300 degrees to radians? How do you convert the polar equation #10 sin(θ)# to the rectangular form? How do you convert the rectangular equation to polar form x=4? How do you find the cartesian graph of #r cos(θ) = 9#? See all questions in Converting Between Systems Impact of this question 1311 views around the world You can reuse this answer Creative Commons License