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A circle in the xy‑plane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?
- a)(−7, 3)
- b)(−3, 1)
- c)(0, 0)
- d)(3, 2)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. W...
Choice D is correct. The circle with equation (x + 3)2 + (y – 1)2 = 25 has center (–3, 1) 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 (3, 2) and (–3, 1) is
which is greater than 5.
Therefore, (3, 2) does NOT lie in the interior of the circle. Choice A is incorrect. The distance between (–7, 3) and (–3, 1) is
which is less than 5, and therefore (–7, 3) 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 (0, 0) and (–3, 1) is
which is less than 5, and therefore (0, 0) lies in the interior of the circle.
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 (3, 2) and (–3, 1) is
which is greater than 5.Therefore, (3, 2) does NOT lie in the interior of the circle. Choice A is incorrect. The distance between (–7, 3) and (–3, 1) is
which is less than 5, and therefore (–7, 3) 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 (0, 0) and (–3, 1) is
which is less than 5, and therefore (0, 0) lies in the interior of the circle.Free Test
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Community Answer
A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. W...
To find the equation of a circle in the xy-plane, we need the coordinates of the center and the radius.
From the given equation, we can see that the center of the circle is at (3, -2) because the terms (x - 3)^2 and (y + 2)^2 represent the squares of the differences between x and 3, and y and -2, respectively.
The radius of the circle can be found by taking the square root of the constant term on the right side of the equation. In this case, the constant term is 9, so the radius is √9 = 3.
Therefore, the equation of the circle is (x - 3)^2 + (y + 2)^2 = 9.
From the given equation, we can see that the center of the circle is at (3, -2) because the terms (x - 3)^2 and (y + 2)^2 represent the squares of the differences between x and 3, and y and -2, respectively.
The radius of the circle can be found by taking the square root of the constant term on the right side of the equation. In this case, the constant term is 9, so the radius is √9 = 3.
Therefore, the equation of the circle is (x - 3)^2 + (y + 2)^2 = 9.
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A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer?
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A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer?.
A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle in the xyplane has equation (x + 3)2 + (y − 1)2 = 25. Which of the following points does NOT lie in the interior of the circle?a)(−7, 3)b)(−3, 1)c)(0, 0)d)(3, 2)Correct answer is option 'D'. Can you explain this answer?.
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