How do you convert $r=4sec(theta)(1+ tan(theta))$ into cartesian form?

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Answer 1 · 2016-10-26T09:53:48

$1/4=1/x+1/y$

Polar coordinates $(r,theta)$ and Cartesian coordinates $(x,y)$ are related as

$x=rcostheta$ and $y=rsintheta$ , i.e. $tantheta=y/x$

Hence, $r=4sectheta(1+tantheta)$ can be written as

$rcostheta=4(1+tantheta)$

or $y=4(1+y/x)$

or $xy=4x+4y$

or $(xy)/(4xy)=(4x)/(4xy)+(4y)/(4xy)$

or $1/4=1/y+1/x$ or $1/4=1/x+1/y$

How do you convert r=4sec(theta)(1+ tan(theta))r=4sec(theta)(1+ tan(theta)) into cartesian form?