003 Which equation represents the circle whose center is (-2, 3) and whose radius is 5? 1) (x- 2)? + (y+ 3)? = 5 2) (x+ 2)? + (- 3)? = 5 3) (x+ 2)? + (v- 3)° - 25 4) (x- 2)° + (v + 3)° = 25
003 Which equation represents the circle whose center is (-2, 3) and whose radius is 5? 1) (x- 2)? + (y+ 3)? = 5 2) (x+ 2)? + (- 3)? = 5 3) (x+ 2)? + (v- 3)° - 25 4) (x- 2)° + (v + 3)° = 25
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Problem 003:**
**Question:**
Which equation represents the circle whose center is \((-2, 3)\) and whose radius is 5?
**Answer choices:**
1. \((x - 2)^2 + (y + 3)^2 = 5\)
2. \((x + 2)^2 + (y - 3)^2 = 5\)
3. \((x + 2)^2 + (y - 3)^2 = 25\)
4. \((x - 2)^2 + (y + 3)^2 = 25\)
**Explanation:**
To determine which equation correctly represents the given circle, recall the standard form of the equation of a circle:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For the circle in question:
- The center is \((-2, 3)\), so \(h = -2\) and \(k = 3\).
- The radius is \(5\), so \(r = 5\), and thus \(r^2 = 25\).
Substituting the given values into the standard form equation:
\[
(x - (-2))^2 + (y - 3)^2 = 5^2
\]
\[
(x + 2)^2 + (y - 3)^2 = 25
\]
Among the answer choices, option 3 matches this equation:
3. \((x + 2)^2 + (y - 3)^2 = 25\)
Therefore, the correct answer is option 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42779bdc-66e8-47e8-8a59-0cd69b39b8c3%2Fd835ae32-5d2b-4a9c-9e78-27a7f0deb682%2Fvoyt8xb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 003:**
**Question:**
Which equation represents the circle whose center is \((-2, 3)\) and whose radius is 5?
**Answer choices:**
1. \((x - 2)^2 + (y + 3)^2 = 5\)
2. \((x + 2)^2 + (y - 3)^2 = 5\)
3. \((x + 2)^2 + (y - 3)^2 = 25\)
4. \((x - 2)^2 + (y + 3)^2 = 25\)
**Explanation:**
To determine which equation correctly represents the given circle, recall the standard form of the equation of a circle:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For the circle in question:
- The center is \((-2, 3)\), so \(h = -2\) and \(k = 3\).
- The radius is \(5\), so \(r = 5\), and thus \(r^2 = 25\).
Substituting the given values into the standard form equation:
\[
(x - (-2))^2 + (y - 3)^2 = 5^2
\]
\[
(x + 2)^2 + (y - 3)^2 = 25
\]
Among the answer choices, option 3 matches this equation:
3. \((x + 2)^2 + (y - 3)^2 = 25\)
Therefore, the correct answer is option 3.
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