Find an equivalent equation in rectangular coordinates.
-$$\mathrm { r } = 1 + 2 \sin \theta$$
A) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 y$
B) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 y$
C) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 x$
D) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 x$

Question

Quizplus · Accepted Answer

To convert the polar equation $r = 1 + 2\sin\theta$ to rectangular coordinates, use the relationships $r^2 = x^2 + y^2$, $r = \sqrt{x^2 + y^2}$, and $\sin\theta = \frac{y}{r}$. Substituting these into the given equation yields $r = 1 + 2\frac{y}{r}$, which simplifies to $r = \sqrt{x^2 + y^2} = 1 + 2y$, or $x^2 + y^2 = \sqrt{x^2 + y^2} + 2y$.

Find an Equivalent Equation in Rectangular Coordinates r=1+2sin⁡θ\mathrm { r } = 1 + 2 \sin \thetar=1+2sinθ

Find an Equivalent Equation in Rectangular Coordinates $\mathrm { r } = 1 + 2 \sin \theta$