How do you convert polar equations to Cartesian equation given #r sec theta = 3#?

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Answer 1 · 2018-06-26T11:37:37

# (x-3/2)^2 + y^2 = 9/4 #

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 #