Convert the equation $r = 3 \cos \theta$ to rectangular coordinates.
A) $x ^ { 2 } + 3 x + y ^ { 2 } = 0$
B) $x ^ { 2 } + y ^ { 2 } - 3 y = 0$
C) $x ^ { 2 } + y ^ { 2 } + 3 y = 0$
D) $x ^ { 2 } - 3 x + y ^ { 2 } = 0$

Question

Quizplus · Accepted Answer

The polar equation $r = 3 \cos \theta$ can be converted to rectangular coordinates using $x = r \cos \theta$ and $y = r \sin \theta$. Substituting $r = \sqrt{x^2 + y^2}$ and $\cos \theta = \frac{x}{r}$, we get $r = 3 \frac{x}{r}$, which simplifies to $x^2 - 3x + y^2 = 0$.

Convert the Equation r=3cos⁡θr = 3 \cos \thetar=3cosθ To Rectangular Coordinates x2+3x+y2=0x ^ { 2 } + 3 x + y ^ { 2 } = 0x2+3x+y2=0

Convert the Equation $r = 3 \cos \theta$ To Rectangular Coordinates $x ^ { 2 } + 3 x + y ^ { 2 } = 0$