The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).
-$$x ^ { 2 } + 4 y ^ { 2 } = 4$$
A) $4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta = 4 \mathrm { r }$
B) $\cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta = 4 \mathrm { r }$
C) $r ^ { 2 } \left( \cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta \right) = 4$
D) $\mathrm { r } ^ { 2 } \left( 4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta \right) = 4$

Question

Quizplus · Accepted Answer

To convert the given equation $x^2 + 4y^2 = 4$ into polar coordinates, we use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $r^2\cos^2\theta + 4r^2\sin^2\theta = 4$, which simplifies to $r^2(\cos^2\theta + 4\sin^2\theta) = 4$.

The Letters X and Y Represent Rectangular Coordinates x2+4y2=4x ^ { 2 } + 4 y ^ { 2 } = 4x2+4y2=4

The Letters X and Y Represent Rectangular Coordinates $x ^ { 2 } + 4 y ^ { 2 } = 4$