Answer
Polar equation:
$r =± \sqrt {\frac{9}{cos(2 θ)}}$
Graph:
Work Step by Step
Remember: (I) x = rcos( θ) and (II) y = rsin( θ);
(III) $cos(2 θ) = cos^2( θ) - sin^2( θ)$
Use the equations (I) and (II) to covert this rectangular equation to a polar one:
$x^2-y^2=9$
$(rcos( θ))^2-(rsin( θ))^2=9$
$r^2cos^2( θ) - r^2sin^2( θ) = 9$
$r^2 (cos^2( θ)-sin^2( θ)) = 9$
(III) $r^2(cos(2 θ))=9$
$r^2 = \frac{9}{cos(2 θ)}$
$r =± \sqrt {\frac{9}{cos(2 θ)}}$
