SOLUTION: Find an equation in x and y for the conic section with polar equation r = 1/ 1+ cos(theta)

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Question 75901: Find an equation in x and y for the conic section with polar equation
r = 1/ 1+ cos(theta)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation in x and y for the conic section with polar equation
r = 1/ 1+ cos(theta)
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Conversions formulas:
x=rcos(theta)
y=rsin(theta)
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r= x^2+y^2
EQUATION:
r = 1/(1+cos(theta)
r = 1/[1+(x/r)]
r = 1/[(r+x)/r]
r = r/(r+x)
1= 1/(r+x)
r+x=1
sqrt(x^2+y^2)+x=1
sqrt(x^2+y^2)=1-x
Square both sides to get:
x^2+y^2=1-2x+x^2
y^2=-2x+1
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Cheers,
Stan H.