How do you convert $r = \frac{1}{1 - cos x}$ $r=1/(1-cosx)$ into rectangular form?

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Answer 1 · 2018-04-22T14:12:19

The equation is $y^{2} = 2 x + 1$ $y^2=2x+1$

Apply the following to convert from polar coordinates $(r, θ)$ $(r,theta)$ to rectangular coordinates $(x, y)$ $(x,y)$ :

${(x=rcostheta),(y=rsintheta),(x^2+y^2=r^2), (theta=arctan(y/x)):}$

Therefore,

$r=1/(1-costheta)$

$r(1-costheta)=1$

$r-rcostheta=1$

$sqrt(x^2+y^2)-x=1$

$sqrt(x^2+y^2)=1+x$

Squaring both sides

$x^2+y^2=x^2+2x+1$

$y^2=2x+1$

graph{y^2-2x-1=0 [-8.89, 8.89, -4.444, 4.445]}

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