Find an equivalent equation in polar coordinates.
-$$x ^ { 2 } - y ^ { 2 } = 4$$
A) $r \cos 2 \theta = 4$
B) $\cos ^ { 2 } \theta - \sin ^ { 2 } \theta = 4$
C) $\cos ^ { 2 } \theta - \sin ^ { 2 } \theta = 4 r$
D) $r ^ { 2 } \cos 2 \theta = 4$

Question

Quizplus · Accepted Answer

The given equation in Cartesian coordinates is $x^2 - y^2 = 4$. In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation gives $r^2\cos^2\theta - r^2\sin^2\theta = 4$, which simplifies to $r^2(\cos^2\theta - \sin^2\theta) = 4$. Using the double angle identity $\cos 2\theta = \cos^2\theta - \sin^2\theta$, we get $r^2 \cos 2\theta = 4$.

Find an Equivalent Equation in Polar Coordinates x2−y2=4x ^ { 2 } - y ^ { 2 } = 4x2−y2=4

Find an Equivalent Equation in Polar Coordinates $x ^ { 2 } - y ^ { 2 } = 4$