Convert the equation $r = 2 \sin \theta$ to rectangular coordinates.
A) $x ^ { 2 } - 2 x + y ^ { 2 } = 0$
B) $x ^ { 2 } + y ^ { 2 } + 2 y = 0$
C) $x ^ { 2 } + y ^ { 2 } - 2 y = 0$
D) $x ^ { 2 } + 2 x + y ^ { 2 } = 0$

Question

Quizplus · Accepted Answer

The polar equation $r = 2 \sin \theta$ can be converted to rectangular coordinates using the identities $x = r \cos \theta$, $y = r \sin \theta$, and $r^2 = x^2 + y^2$. Substituting $r = 2 \sin \theta$ gives $y = \frac{r^2}{2}$. Thus, $x^2 + y^2 = 2y$, which simplifies to $x^2 + y^2 - 2y = 0$.

Convert the Equation r=2sin⁡θr = 2 \sin \thetar=2sinθ To Rectangular Coordinates x2−2x+y2=0x ^ { 2 } - 2 x + y ^ { 2 } = 0x2−2x+y2=0

Convert the Equation $r = 2 \sin \theta$ To Rectangular Coordinates $x ^ { 2 } - 2 x + y ^ { 2 } = 0$