Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. $$r = 6 \sin \theta$$
A) $x ^ { 2 } + y ^ { 2 } = 6 y$
B) $x ^ { 2 } + y ^ { 2 } = 6 x$
C) $x ^ { 2 } + y ^ { 2 } = \frac { x } { 6 }$
D) $x ^ { 2 } + y ^ { 2 } = \frac { y } { 6 }$
E) $x ^ { 2 } + z ^ { 2 } = 6 x$

Question

Quizplus · Accepted Answer

In cylindrical coordinates, $r = \sqrt{x^2 + y^2}$ and $r\sin(\theta) = y$. Substituting $r = 6\sin(\theta)$ gives $\sqrt{x^2 + y^2} = y$, which simplifies to $x^2 + y^2 = 6y$.

Find an Equation in Rectangular Coordinates for the Equation Given r=6sin⁡θr = 6 \sin \thetar=6sinθ

Find an Equation in Rectangular Coordinates for the Equation Given $r = 6 \sin \theta$