Find an equivalent equation in rectangular coordinates.
-$$\mathrm { r } = 10 \sin \theta$$
A) $x ^ { 2 } + y ^ { 2 } = 10 x$
B) $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 x$
C) $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 y$
D) $x ^ { 2 } + y ^ { 2 } = 10 y$

Question

Quizplus · Accepted Answer

The polar equation $ r = 10 \sin \theta $ can be converted to rectangular coordinates using $ r = \sqrt{x^2 + y^2} $ and $ y = r \sin \theta $. Substituting, we get $ \sqrt{x^2 + y^2} = 10 \frac{y}{\sqrt{x^2 + y^2}} $, which simplifies to $ x^2 + y^2 = 10y $.

Find an Equivalent Equation in Rectangular Coordinates r=10sin⁡θ\mathrm { r } = 10 \sin \thetar=10sinθ

Find an Equivalent Equation in Rectangular Coordinates $\mathrm { r } = 10 \sin \theta$