## ladydragon323 r = 2/(r-sin(theta)) convert the given equation to a rectangular equation one year ago one year ago

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1. ZeHanz

The connection between polar and cartesian coordinates is:$x=r \cos \theta$$y=r \sin \theta$or$r^2=x^2+y^2$$\theta=\arctan \frac{ y }{ x }$ Hint: first rewrite the equation as:$r(r-\sin \theta)=2$then $r^2-r \sin \theta=2$then do some substitutions... Just ask if you don't succeed!

2. ZeHanz

If you substitute the values for r^2 and rsin(theta) as stated above, you get: $x^2+y^2-y=2$This is already fine, because it is a rectangular equation. But there is one more step. Complete the square for y:$x^2+(y-\frac{ 1 }{ 2 })^2-\frac{ 1 }{ 4 }=2$Or:$x^2+(y-\frac{ 1 }{ 2 })^2=2\frac{ 1 }{ 4 }$This is the equation of a circle with center (0, 1/2) and radius 3/2! So it is a very simple curve after all...