Replace the Cartesian equation with an equivalent polar equation.
-$$x ^ { 2 } + 4 y ^ { 2 } = 4$$
A) $r ^ { 2 } \left( \cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta \right) = 4$
B) $r ^ { 2 } \left( 4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta \right) = 4$
C) $4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta = 4 \mathrm { r }$
D) $\cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta = 4 \mathrm { r }$

Question

Quizplus · Accepted Answer

In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given Cartesian equation $x^2 + 4y^2 = 4$ yields $r^2\cos^2\theta + 4r^2\sin^2\theta = 4$, which simplifies to choice A.

Replace the Cartesian Equation with an Equivalent Polar Equation x2+4y2=4x ^ { 2 } + 4 y ^ { 2 } = 4x2+4y2=4

Replace the Cartesian Equation with an Equivalent Polar Equation $x ^ { 2 } + 4 y ^ { 2 } = 4$