How do you convert $r=2/(1+sin(theta))$ into cartesian form?

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Answer 1 · 2016-06-20T09:24:45

$x^2+4y-4=0$

If polar coordinates $(r,theta)$ are written as $(x,y)$ in Cartesian coordinates, then

$rcostheta=x$ , $rsintheta=y$ and $r^2=x^2+y^2$

Hence, $r=2/(1+sintheta)$ can be written as

$r=2/(1+y/r)$ or $r+y=2$ or $r=2-y$ and on squaring

$r^2=y^2-4y+4$ i.e. $x^2+y^2=y^2-4y+4$ or

$x^2+4y-4=0$ , which is the equation of a parabola.

graph{x^2+4y-4=0 [-10, 10, -6.8, 3.2]}

How do you convert r=2/(1+sin(theta))r=2/(1+sin(theta)) into cartesian form?