How do you write the equation using rectangular coordinates given $r^2sin2theta=8$ ?

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Answer 1 · 2016-10-04T09:50:27

$xy=4$

The relation between rectangular Cartesian coordinates $(x,y)$ and polar coordinates $(r,theta)$ is given by

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

Hence $r^2sin2theta=8$ can be rewritten as

$r^2xx2sinthetacostheta=8$

or $2xxrsinthetaxxrcostheta=8$

or $2xxyxx x=8$

or $xy=4$

How do you write the equation using rectangular coordinates given r^2sin2theta=8r^2sin2theta=8?