Convert the polar equation to rectangular form. $r = 6 \cos 2 \theta$
A) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$
B) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$
C) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$
D) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$
E) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$

Question

Convert the polar equation to rectangular form.​ $r = 6 \cos 2 \theta$ ​
A) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$
B) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$
C) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$
D) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$
E) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$

Quizplus · Accepted Answer

The polar equation $r = 6 \cos 2\theta$ can be converted to rectangular form using the identities $r^2 = x^2 + y^2$ and $\cos 2\theta = \frac{x^2 - y^2}{x^2 + y^2}$. Substituting these into the equation and simplifying gives $(x^2 + y^2)^3 = 36(x^2 - y^2)^2$.

Convert the Polar Equation to Rectangular Form r=6cos⁡2θr = 6 \cos 2 \thetar=6cos2θ

Convert the Polar Equation to Rectangular Form $r = 6 \cos 2 \theta$