How do you convert #x^2+y^2 - 2y=0# into polar form?

1 Answer
Ken C.
Jul 13, 2016

Make use of a few conversion formulas and simplify. See below.

Explanation:

Recall the following formulas, used for conversion between polar and rectangular coordinates:

  • #x^2+y^2=r^2#
  • #rsintheta=y#

Now take a look at the equation:
#x^2+y^2-2y=0#

Since #x^2+y^2=r^2#, we can replace the #x^2+y^2# in our equation with #r^2#:
#x^2+y^2-2y=0#
#->r^2-2y=0#

Also, because #y=rsintheta#, we can replace the #y# in our equation with #sintheta#:
#r^2-2y=0#
#->r^2-2(rsintheta)=0#

We can add #2rsintheta# to both sides:
#r^2-2(rsintheta)=0#
#->r^2=2rsintheta#

And we can finish by dividing by #r#:
#r^2=2rsintheta#
#->r=2sintheta#

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