A circle in the xy -plane has equation . Which of the following points does NOT lie in the interior

Question

A circle in the xy -plane has equation . Which of the following points does NOT lie in the interior of the circle?

Accepted Answer

Choice D is correct. The circle with equation has center and radius 5. For a point to be inside of the circle, the distance from that point to the center must be less than the radius, 5. The distance between and is , which is greater than 5. Therefore, does NOT lie in the interior of the circle. Choice A is incorrect. The distance between and is , which is less than 5, and therefore lies in the interior of the circle. Choice B is incorrect because it is the center of the circle. Choice C is incorrect because the distance between and is , which is less than 5, and therefore in the interior of the circle.

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