How do you convert #r = 1-2 cosθ# into rectangular forms?

1 Answer
Yonas Yohannes
Jan 24, 2016

#(x^2+y^2- bx)^2 = a^2(x^2+y^2)#
a = 1; b = -2
#(x^2+y^2+ 2x)^2 = (x^2+y^2)#

Explanation:

use the Polar to Cartesian transformation:
#r^2 = x^2 + y^2#
#x = rcostheta #

# r = a + bcostheta#
#r^2 = ar + rbcostheta#
#r^2- rbcostheta =ar#
#x^2+y^2- bx = ar# square the entire thing and write
#(x^2+y^2- bx)^2 = (ar)^2#
#(x^2+y^2- bx)^2 = a^2(x^2+y^2)#

a = 1; b = -2
#(x^2+y^2+ 2x)^2 = (x^2+y^2)#

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