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

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Answer 1 · 2016-07-13T01:15:21

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

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

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 $r$ :
$r^2=2rsintheta$
$->r=2sintheta$

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