Describe the graph of the polar equation.
-$$\mathrm { r } ^ { 2 } = 38 \mathrm { rcos } \theta - 6 r \sin \theta - 9$$
A) Parabola opening upward with vertex (38, -6)
B) Circle with radius 19 and center (19, -3)
C) Circle with radius 3 and center (38, -6)
D) Parabola opening to the right with vertex (38, -6)

Question

Quizplus · Accepted Answer

The given polar equation can be rewritten in Cartesian coordinates by recognizing that $r^2 = x^2 + y^2$, $r\cos\theta = x$, and $r\sin\theta = y$. Substituting these into the equation gives $x^2 + y^2 = 38x - 6y - 9$. Rearranging terms to complete the squares, we get $(x - 19)^2 + (y + 3)^2 = 19^2$, which describes a circle with radius 19 and center at (19, -3).

Describe the Graph of the Polar Equation r2=38rcosθ−6rsin⁡θ−9\mathrm { r } ^ { 2 } = 38 \mathrm { rcos } \theta - 6 r \sin \theta - 9r2=38rcosθ−6rsinθ−9

Describe the Graph of the Polar Equation $\mathrm { r } ^ { 2 } = 38 \mathrm { rcos } \theta - 6 r \sin \theta - 9$