How do you convert #r=2/(1+sin(theta))# into cartesian form?

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Answer 1 · 2016-06-20T09:24:45

#x^2+4y-4=0#

If polar coordinates #(r,theta)# are written as #(x,y)# in Cartesian coordinates, then

#rcostheta=x#, #rsintheta=y# and #r^2=x^2+y^2#

Hence, #r=2/(1+sintheta)# can be written as

#r=2/(1+y/r)# or #r+y=2# or #r=2-y# and on squaring

#r^2=y^2-4y+4# i.e. #x^2+y^2=y^2-4y+4# or

#x^2+4y-4=0#, which is the equation of a parabola.

graph{x^2+4y-4=0 [-10, 10, -6.8, 3.2]}