SOLUTION: Convert the polar equation to rectangular form: r=-2sin(theta) Thanks!!

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Question 468905: Convert the polar equation to rectangular form:
r=-2sin(theta)
Thanks!!
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Use the following relationships:
x+=+r%2Acos%28theta%29
y+=+r%2Asin%28theta%29
r+=+sqrt%28x%5E2+%2B+y%5E2%29
Now substitute into given equation:
r+=+-2%2Asin%28theta%29
Notice we can solve for sin(theta)
sin%28theta%29+=+y%2Fr+=+y%2Fsqrt%28x%5E2+%2B+y%5E2%29
Thus equation becomes
sqrt%28x%5E2+%2B+y%5E2%29+=+-2%2A%28y%2Fsqrt%28x%5E2+%2B+y%5E2%29%29
Multiply by sqrt(x^2 + y^2) on both sides
x%5E2+%2B+y%5E2+=+-2y
Add 2y to both sides
x%5E2+%2B+y%5E2+%2B2y+=+0
Use completing the square to obtain standard circle equation
x%5E2+%2B+y%5E2+%2B+2y+%2B1+=+1
x%5E2+%2B+%28y%2B1%29%5E2+=+1
Therefore polar equation is converted to rectangular form and is the graph of a circle of radius 1 centered at (0,-1).