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What is the center of the circle with equation (x - 3)2 + (y + 3)2 = 4 in the standard (x, y) coordinate plane?
- a)(3, 3)
- b)(3, −3)
- c)(√3, −√3)
- d)(−3, 3)
- e)(−√3, √3)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
What is the center of the circle with equation (x - 3)2 + (y + 3)2 = 4...
To solve this problem, you need to know that the equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2.
Therefore, the center of the circle in the problem, (x − 3)2 + (y + 3)2 = 4, is (3, −3).
Therefore, the center of the circle in the problem, (x − 3)2 + (y + 3)2 = 4, is (3, −3).
Community Answer
What is the center of the circle with equation (x - 3)2 + (y + 3)2 = 4...
Understanding the Circle Equation
To find the center of the circle given by the equation (x - 3)² + (y + 3)² = 4, we need to recognize the standard form of a circle's equation, which is:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the center of the circle, and r is the radius.
Identifying the Components
From the equation (x - 3)² + (y + 3)² = 4, we can identify:
- The term (x - 3) indicates that h = 3.
- The term (y + 3) can be rewritten as (y - (-3)), which indicates that k = -3.
- The right side of the equation, 4, represents r², meaning the radius r = 2 (since r = √4).
Determining the Center
Now we can determine the center of the circle:
- Center (h, k) = (3, -3)
Thus, the center of the circle is at the point (3, -3).
Conclusion
Therefore, the correct answer to the question regarding the center of the circle is option 'B' (3, -3).
To find the center of the circle given by the equation (x - 3)² + (y + 3)² = 4, we need to recognize the standard form of a circle's equation, which is:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the center of the circle, and r is the radius.
Identifying the Components
From the equation (x - 3)² + (y + 3)² = 4, we can identify:
- The term (x - 3) indicates that h = 3.
- The term (y + 3) can be rewritten as (y - (-3)), which indicates that k = -3.
- The right side of the equation, 4, represents r², meaning the radius r = 2 (since r = √4).
Determining the Center
Now we can determine the center of the circle:
- Center (h, k) = (3, -3)
Thus, the center of the circle is at the point (3, -3).
Conclusion
Therefore, the correct answer to the question regarding the center of the circle is option 'B' (3, -3).
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What is the center of the circle with equation (x - 3)2 + (y + 3)2 = 4 in the standard (x, y) coordinate plane?a)(3, 3)b)(3, −3)c)(√3, −√3)d)(−3, 3)e)(−√3, √3)Correct answer is option 'B'. Can you explain this answer?
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