Find an equivalent equation in rectangular coordinates.
-$r - 6 \sin \theta = 4 \cos \theta$
A) $\sqrt { x ^ { 2 } + y ^ { 2 } } - 6 y = 4 x$
B) $x ^ { 2 } + y ^ { 2 } - 6 y = 4 x$
C) $x ^ { 2 } + y ^ { 2 } + 6 y = 4 x$
D) $x ^ { 2 } + y ^ { 2 } = 0$

Question

Quizplus · Accepted Answer

The polar equation $r - 6 \sin \theta = 4 \cos \theta$ can be converted to rectangular coordinates using $r = \sqrt{x^2 + y^2}$, $\sin \theta = \frac{y}{r}$, and $\cos \theta = \frac{x}{r}$. Substituting these into the equation and simplifying gives $x^2 + y^2 - 6y = 4x$.

Find an Equivalent Equation in Rectangular Coordinates r−6sin⁡θ=4cos⁡θr - 6 \sin \theta = 4 \cos \thetar−6sinθ=4cosθ

Find an Equivalent Equation in Rectangular Coordinates $r - 6 \sin \theta = 4 \cos \theta$