Describe the graph of the polar equation.
-$$r ^ { 2 } = 46 r \cos \theta$$
A) Circle of radius 23 and center (23, 0)
B) Vertical line passing through (46, 0)
C) Circle of radius 23 and center (0, 23)
D) Horizontal line passing through (0, 46)

Question

Quizplus · Accepted Answer

To convert the given polar equation to Cartesian coordinates, we use the relations $x = r \cos \theta$ and $y = r \sin \theta$. The given equation is $r^2 = 46r\cos\theta$. Dividing both sides by $r$ (assuming $r \neq 0$), we get $r = 46\cos\theta$. Substituting the Cartesian relations, we get $r = 46\frac{x}{r}$, which simplifies to $r^2 = 46x$. Converting $r^2$ to Cartesian coordinates gives $x^2 + y^2 = 46x$. Rearranging, $x^2 - 46x + y^2 = 0$, and completing the square for $x$, we get $(x - 23)^2 + y^2 = 23^2$, which is the equation of a circle with radius 23 and center at (23, 0).

Describe the Graph of the Polar Equation r2=46rcos⁡θr ^ { 2 } = 46 r \cos \thetar2=46rcosθ

Describe the Graph of the Polar Equation $r ^ { 2 } = 46 r \cos \theta$