Answer
$y^{2}-3x^{2}=0$
Work Step by Step
Formulas relating rectangular $(x,y)$ and polar $(r,\theta)$ coordinates:
$ x=r\cos\theta$ and $ y=r\sin\theta$
$r^{2}=x^{2}+y^{2}$ and $\displaystyle \tan\theta=\frac{y}{x}$.
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$\sec\theta=2$
$\displaystyle \frac{1}{\cos\theta}=2\qquad/\times\cos\theta$
$1=2\cos\theta\qquad/\times r$
$r=2r\cos\theta\qquad $...substitute $ r\cos\theta$ with x
$ r=2x\qquad$... square both sides
$ r^{2}=4x^{2}\qquad$...substitute $r^{2}$
$x^{2}+y^{2}=4x^{2}\qquad /-4x^{2}$
$y^{2}-3x^{2}=0$
