How do you convert polar equations to Cartesian equation given #r sec theta = 3#? Trigonometry The Polar System Converting Between Systems 1 Answer Rhys Jun 26, 2018 # (x-3/2)^2 + y^2 = 9/4 # Explanation: Use our polar knowledge: #r^2 = x^2 + y^2 # #rcostheta = x " and " rsintheta = y # #rsectheta = 3 # #=> r/costheta =3 # #=> r = 3costheta # #=> r^2 = 3rcostheta # #=> x^2 + y^2 = 3x # #=> x^2 - 3x + 9/4 + y^2 = 9/4# #=> (x-3/2)^2 + y^2 = 9/4 # 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 10667 views around the world You can reuse this answer Creative Commons License