Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 4$
A) $r= 4 \csc 2 \theta$
B) $r = 2 \csc \theta$
C) $r= 2 \sec 2 \theta$
D) $r ^ { 2 } = 4 \sec 2 \theta$
E)none of these

Question

Quizplus · Accepted Answer

We start by using the conversion formulas

$x = r \cos 	heta$
$y = r \sin 	heta$

Substituting these in the equation, we get

$r^2\cos^2 	heta - r^2 \sin^2 	heta = 4$

$r^2(\cos^2 	heta - \sin^2 	heta) = 4$

$r^2\cos 2	heta = 4$

$r = 2\sec 2	heta$

Squaring both sides, we get

$r^2 = 4\sec^2 2	heta$

Substituting $\gamma$ for $r^2$, we get

$\gamma^2 = 4 \sec 2 	heta$

Therefore, the answer is D.

Convert the Equation to Polar Form x2−y2=4x ^ { 2 } - y ^ { 2 } = 4x2−y2=4

Convert the Equation to Polar Form $x ^ { 2 } - y ^ { 2 } = 4$