Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 9$
A) $r ^ { 2 } = 9 \csc 2 \theta$
B) $r = 3 \sec 2 \theta$
C) $r ^ { 2 } = 9 \sec 2 \theta$
D) $r ^ { 2 } = 9 \csc \theta$
E)none of these

Question

Quizplus · Accepted Answer

We start by using the conversion formulas $x=r\cos	heta$ and $y=r\sin	heta$. Substituting these into the equation gives:
$r^2\cos^2	heta-r^2\sin^2	heta=9$
After simplifying,
$r^2(\cos^2	heta-\sin^2	heta)=9$
$r^2\cos2	heta=9$
Therefore, the polar form of the equation is $r^2=9\sec2	heta$, which matches choice C.

Convert the Equation to Polar Form x2−y2=9x ^ { 2 } - y ^ { 2 } = 9x2−y2=9

Convert the Equation to Polar Form $x ^ { 2 } - y ^ { 2 } = 9$