Convert the polar equation to rectangular coordinates. $r + \cos \theta = 3$
A) $\left( x ^ { 2 } + y ^ { 2 } - 3 x \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$
B) $x ^ { 2 } + y ^ { 2 } = 9 ( x + y )$
C) $\left( x ^ { 2 } + y ^ { 2 } - x \right) ^ { 2 } = 3 \left( x ^ { 2 } - y ^ { 2 } \right)$
D) $\left( x ^ { 2 } + y ^ { 2 } + 2 x \right) ^ { 2 } = 3 ( x + y )$
E)none of these

Question

Quizplus · Accepted Answer

The given polar equation is $r + \cos \theta = 3$. To convert it into rectangular coordinates, we use the relations $r^2 = x^2 + y^2$, $r\cos\theta = x$, and $r\sin\theta = y$. Substituting $r = \sqrt{x^2 + y^2}$ and $\cos\theta = x/r$, we get $\sqrt{x^2 + y^2} + x/\sqrt{x^2 + y^2} = 3$. None of the provided options correctly represents this equation after simplification.

Convert the Polar Equation to Rectangular Coordinates r+cos⁡θ=3r + \cos \theta = 3r+cosθ=3

Convert the Polar Equation to Rectangular Coordinates $r + \cos \theta = 3$