SOLUTION: convert rectangular equation to polar equation x^2+(y-5)^2=25

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Question 610913: convert rectangular equation to polar equation x^2+(y-5)^2=25
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28y-5%29%5E2=25
First let's simplify/ Squaring y-5:
x%5E2%2By%5E2-10y%2B25=25
Subtracting 25 from each side we get:
x%5E2%2By%5E2-10y=0

Now let's convert to polar form. Replacing x with r%2Acos%28theta%29 and y with r%2Asin%28theta%29 this becomes:

Simplifying:
r%5E2%2Acos%5E2%28theta%29+%2B+r%5E2%2Asin%5E2%28theta%29+-+10r%2Asin%28theta%29+=+0
Factoring out r%5E2 from the first two terms:
r%5E2%28cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%29+-+10r%2Asin%28theta%29+=+0
Since cos%5E2%28theta%29+%2B+sin%5E2%28theta%29+=+1:
r%5E2%281%29+-+10r%2Asin%28theta%29+=+0
which simplifies to:
r%5E2+-+10r%2Asin%28theta%29+=+0
Since r cannot be zero, we can divide both sides by r giving:
r+-+10sin%28theta%29+=+0
This may be an acceptable answer. Or you could add 10sin%28theta%29 to each side:
r+=+10sin%28theta%29