How do you write the rectangular equation $x^{2} + y^{2} = 2 y$ $x^2+y^2=2y$ in polar form?

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Answer 1 · 2016-10-27T11:15:03

$r = 2 sin θ$ $r=2sintheta$

For Polar co-ords.

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$

$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

So $x^{2} + y^{2} = 2 y$ $x^2+y^2=2y$

becomes

$r^{2} = 2 r sin θ$ $r^2=2rsintheta$

$r^cancel(2)=2cancel(r)sintheta$

$:.r=2sintheta$

How do you write the rectangular equation x^2+y^2=2yx2+y2=2yx^2+y^2=2y in polar form?