How do you convert $r^2= sec2theta$ to polar form?

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Answer 1 · 2017-01-27T17:42:13

$x^2-y^2=1$

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

$x=rcostheta$ , $y=rsintheta$ i.e. $x^2+y^2=r^2$

Hence $r^2=sec2theta$ can be written as

$r^2=1/(cos2theta)=1/(cos^2theta-sin^2theta)$

or $r^2cos^2theta-r^2sin^2theta=1$

or $x^2-y^2=1$
graph{x^2-y^2=1 [-10, 10, -5, 5]}

How do you convert r^2= sec2thetar^2= sec2theta to polar form?