Answer
$3x^2-y^2-16x+16=0$,
Hyperbola.
Work Step by Step
$r=\frac{8}{2+4cos\theta}$,
$r=\frac{4}{1+2cos\theta}$,
$r+2r\ cos\theta=4$,
$r=4-2\ cos\theta$,
$r^2=(4-2\ cos\theta)^2$,
$x^2+y^2=(4-2x)^2$,
$3x^2-y^2-16x+16=0$,
Hyperbola.
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