Describe the graph of the polar equation.
-$$\mathrm { r } ^ { 2 } \sin 2 \theta = 22$$
A) Hyperbola with the $x$ - and $y$-axes as asymptotes
B) Hyperbola with asymptotes $y = \pm 11 x$
C) Parabola centered at the origin opening to the right
D) Parabola centered at the origin opening upward

Question

Quizplus · Accepted Answer

The given polar equation can be rewritten in Cartesian coordinates by using the identities $r^2 = x^2 + y^2$ and $\sin 2\theta = \frac{2xy}{r^2}$. Substituting these into the equation gives $2xy = 22$, or $xy = 11$, which represents a hyperbola with the $x$- and $y$-axes as asymptotes.

Describe the Graph of the Polar Equation r2sin⁡2θ=22\mathrm { r } ^ { 2 } \sin 2 \theta = 22r2sin2θ=22

Describe the Graph of the Polar Equation $\mathrm { r } ^ { 2 } \sin 2 \theta = 22$