SOLUTION: convert the equation from polar to rectangular {{{r=2/(1-sin(theta))}}}

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Question 1134405: convert the equation from polar to rectangular
r=2%2F%281-sin%28theta%29%29
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
r=2%2F%281%2Bsin%28theta%29%29%2A%281-sin%28theta%29%29%2F%281-sin%28theta%29%29
r=%282-2sin%28theta%29%29%2F%281-sin%5E2%28theta%29%29
r=%282-2sin%28theta%29%29%2F%28cos%5E2%28theta%29%29
r%5E2=%282r-2rsin%28theta%29%29%2F%28cos%5E2%28theta%29%29
r%5E2%28cos%5E2%28theta%29%29=2r-2rsin%28theta%29
%28rcos%28theta%29%29%5E2=2r-2rsin%28theta%29
Substitute y=rsin%28theta%29, x=rcos%28theta%29, and r=sqrt%28x%5E2%2By%5E2%29
x%5E2=2sqrt%28x%5E2%2By%5E2%29-2y
x%5E2%2F2%2By=sqrt%28x%5E2%2By%5E2%29
x%5E4%2F4%2Byx%5E2%2By%5E2=x%5E2%2By%5E2
x%5E4%2F4%2Byx%5E2=x%5E2
x%5E2%28x%5E2%2F4%2By%29=x%5E2
x%5E2%2F4%2By=1
y=-x%5E2%2F4%2B1


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