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

Question

Quizplus · Accepted Answer

To convert the given polar equation $r = 2 ( \sin \theta - \cos \theta )$ to rectangular coordinates, use the relationships $x = r \cos \theta$ and $y = r \sin \theta$. Substituting $r = \sqrt{x^2 + y^2}$, the equation becomes $\sqrt{x^2 + y^2} = 2(y - x)$. Squaring both sides gives $x^2 + y^2 = 4(y^2 - 2xy + x^2)$, simplifying to $x^2 + y^2 = 2y - 2x$.

Find an Equivalent Equation in Rectangular Coordinates r=2(sin⁡θ−cos⁡θ)r = 2 ( \sin \theta - \cos \theta )r=2(sinθ−cosθ)

Find an Equivalent Equation in Rectangular Coordinates $r = 2 ( \sin \theta - \cos \theta )$