What is the equation of this circle in standard form? O (+1)² + (y-1)² = 2 0 (x-1)² + (y + 1)² = 5 ○ (x− 1)² + (y+1)² = 25 O (x + 1)² + (y-1)² = 5 10-9-8-7 -5 4 -3-2-1 10- 9- -3- 10 4 8 5 4+ 3 2 44 7 -11 -2+ -6 -7- 1 4 5 9. 7 8 9 10
What is the equation of this circle in standard form? O (+1)² + (y-1)² = 2 0 (x-1)² + (y + 1)² = 5 ○ (x− 1)² + (y+1)² = 25 O (x + 1)² + (y-1)² = 5 10-9-8-7 -5 4 -3-2-1 10- 9- -3- 10 4 8 5 4+ 3 2 44 7 -11 -2+ -6 -7- 1 4 5 9. 7 8 9 10
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
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![**Question:** What is the equation of this circle in standard form?
**Options:**
- \( \big( x + 1 \big)^2 + \big( y - 1 \big)^2 = 25 \)
- \( \big( x - 1 \big)^2 + \big( y + 1 \big)^2 = 5 \)
- \( \big( x - 1 \big)^2 + \big( y + 1 \big)^2 = 25 \)
- \( \big( x + 1 \big)^2 + \big( y - 1 \big)^2 = 5 \)
**Graph Description:**
This is a coordinate plane with axes labeled from -10 to 10 on both x and y axes. In the graph, there is a circle centered at the point \((1, -1)\) with a radius of 5 units. The circle intersects the y-axis at \(2\) and \(-4\), and it intersects the x-axis at \(-4\) and \(6\).
To determine the standard form of the equation of the circle, recall that the standard form is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center \((1, -1)\) and radius \(5\), the equation of the circle is:
\[ (x - 1)^2 + (y + 1)^2 = 25 \]
Therefore, the correct option is:
\[ (x - 1)^2 + (y + 1)^2 = 25 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2Fca5c3f5d-2744-4006-a290-f560e18c27b4%2F39svka_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:** What is the equation of this circle in standard form?
**Options:**
- \( \big( x + 1 \big)^2 + \big( y - 1 \big)^2 = 25 \)
- \( \big( x - 1 \big)^2 + \big( y + 1 \big)^2 = 5 \)
- \( \big( x - 1 \big)^2 + \big( y + 1 \big)^2 = 25 \)
- \( \big( x + 1 \big)^2 + \big( y - 1 \big)^2 = 5 \)
**Graph Description:**
This is a coordinate plane with axes labeled from -10 to 10 on both x and y axes. In the graph, there is a circle centered at the point \((1, -1)\) with a radius of 5 units. The circle intersects the y-axis at \(2\) and \(-4\), and it intersects the x-axis at \(-4\) and \(6\).
To determine the standard form of the equation of the circle, recall that the standard form is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center \((1, -1)\) and radius \(5\), the equation of the circle is:
\[ (x - 1)^2 + (y + 1)^2 = 25 \]
Therefore, the correct option is:
\[ (x - 1)^2 + (y + 1)^2 = 25 \]
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