SOLUTION: What is x² + y² - 12y = 0 in polar form? Thanks.

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Question 1080811: What is x² + y² - 12y = 0 in polar form? Thanks.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2+%2B+y%5E2+-12y+=+0 to polar form:
Remember the conversions between Cartesian and polar.
r%5E2+=+x%5E2+%2B+y%5E2
y+=+r%2Asin%28theta%29
x+=+r%2Acos%28theta%29

Now let's convert.
x%5E2+%2B+y%5E2+-12y+=+0
%28r%2Acos%28theta%29%29%5E2+%2B+%28r%2Asin%28theta%29%29%5E2+-12r%2Asin%28theta%29+=+0
%28r%5E2%2Acos%5E2%28theta%29+%2B+r%5E2%2Asin%5E2%28theta%29%29+-12r%2Asin%28theta%29+=+0
r%5E2%28cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%29+-12r%2Asin%28theta%29+=+0
r%5E2%281%29+-12r%2Asin%28theta%29+=+0
r%5Ecross%282%29++=+12cross%28r%29%2Asin%28theta%29
r++=+12%2Asin%28theta%29