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Geometry and Trigonometry Difficulty: Easy

${(x - 6)}^{2} + {(y - 3)}^{2} = 81$

The graph of the given equation in the xy-plane is a circle. What is the length of the radius of this circle?

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Explanation

Choice C is correct. The equation of a circle in the xy-plane can be written as ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ , where the center of the circle is $(h, k)$ and the radius of the circle is $r$ . The graph of the given equation, ${(x - 6)}^{2} + {(y - 3)}^{2} = 81$ , is a circle in the xy-plane. This equation can be written as ${(x - 6)}^{2} + {(y - 3)}^{2} = 9^{2}$ , where $h equals 6$ , $k equals 3$ , and $r equals 9$ . Therefore, the radius of this circle is $9$ .

Choice A is incorrect. This is the y-coordinate of the center, not the radius, of the circle defined by the given equation.

Choice B is incorrect. This is the x-coordinate of the center, not the radius, of the circle defined by the given equation.

Choice D is incorrect. This is the value of the radius squared, not the radius, of the circle defined by the given equation.