How do you convert $x y = 4$ $xy = 4$ into polar form?

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Answer 1 · 2016-04-18T08:12:02

$r^{2} = 8 csc 2 θ$ $r^2=8csc 2theta$

$x = r cos θ and y = r sin θ$ $x = r cos theta and y = r sin theta$ .
$r^{2} sin θ cos θ = 4$ $r^2sin theta cos theta=4$ .

Using $sin 2 θ = 2 sin θ cos θ$ $sin 2theta = 2 sin theta cos theta$ ,
$r^{2} = 8 csc 2 θ$ $r^2=8csc 2theta$

This is the polar equation of a rectangular hyperbola, with axes of co-ordinates as asymptotes.

How do you convert xy = 4xy=4xy = 4 into polar form?