Replace the polar equation with an equivalent Cartesian equation.
-$$\mathrm { r } ^ { 2 } \sin 2 \theta = 32$$
A) $y = \frac { 32 } { x }$
B) $y = 32 x ^ { 2 }$
C) $y = 16 x$
D) $y = \frac { 16 } { x }$

Question

Quizplus · Accepted Answer

The polar equation $r^2 \sin 2\theta = 32$ can be converted to Cartesian coordinates by using the identities $r^2 = x^2 + y^2$ and $\sin 2\theta = \frac{2y}{r}$. Substituting these into the given equation, we get $r^2 \cdot \frac{2y}{r} = 32$, which simplifies to $2xy = 32$ or $y = \frac{16}{x}$.

Replace the Polar Equation with an Equivalent Cartesian Equation r2sin⁡2θ=32\mathrm { r } ^ { 2 } \sin 2 \theta = 32r2sin2θ=32

Replace the Polar Equation with an Equivalent Cartesian Equation $\mathrm { r } ^ { 2 } \sin 2 \theta = 32$