How do you convert the rectangular equation #(y-2)^2+x^2=4# into polar form?

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Answer 1 · 2017-01-16T20:37:19

Expand the square
Substitute #r^2# for #x^2 + y^2# and #rsin(theta)# for y
Combine like terms
Divide both sides by r
Express r in terms of #theta#

Expand the square:

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

Substitute #r^2# for #x^2 + y^2# and #rcos(theta)# for y:

#r^2 -4rsin(theta) + 4 = 4#

Combine like terms:

#r^2 -4rsin(theta) = 0#

Divided both sides by r:

#r -4sin(theta) = 0#

Express r in terms of theta:

#r = 4sin(theta)#