Write the equation of the circle that is tangent to the y-axis. Its centre is at (-3,5). (x+3)² + (y – 5)² = 9 O (x − 3)² + (y + 5)² = 3 (x − 3)² + (y + 5)² = 9 (x + 3)² + (y − 5)² = 3 -
Write the equation of the circle that is tangent to the y-axis. Its centre is at (-3,5). (x+3)² + (y – 5)² = 9 O (x − 3)² + (y + 5)² = 3 (x − 3)² + (y + 5)² = 9 (x + 3)² + (y − 5)² = 3 -
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.4: Writing And Graphing Equations Of Lines
Problem 80E
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Question
![**Question: Write the equation of the circle that is tangent to the y-axis. Its centre is at (-3, 5).**
Options:
1. \( (x + 3)^2 + (y - 5)^2 = 9 \)
2. \( (x - 3)^2 + (y + 5)^2 = 3 \)
3. \( (x - 3)^2 + (y + 5)^2 = 9 \)
4. \( (x + 3)^2 + (y - 5)^2 = 3 \)
---
**Explanation:**
To write the equation of a circle, we use the standard form:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given:
- Center \((h, k) = (-3, 5)\)
- The circle is tangent to the y-axis, meaning the distance from the center to the y-axis is equal to the radius \(r\).
The radius \(r\) will be the absolute value of the x-coordinate of the center since it is tangent to the y-axis.
So,
\[ r = |-3| = 3 \]
Thus, the equation of the circle is:
\[ (x + 3)^2 + (y - 5)^2 = 3^2 \]
\[ (x + 3)^2 + (y - 5)^2 = 9 \]
Therefore, the correct option is:
- \( (x + 3)^2 + (y - 5)^2 = 9 \)
This option corresponds to the first choice in the given list.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F361784a8-d964-492d-9687-5d5c5e192aef%2F7e3d0d55-3050-43b4-9a11-3c366bc3c5d0%2F3jskcvoh_processed.png&w=3840&q=75)
Transcribed Image Text:**Question: Write the equation of the circle that is tangent to the y-axis. Its centre is at (-3, 5).**
Options:
1. \( (x + 3)^2 + (y - 5)^2 = 9 \)
2. \( (x - 3)^2 + (y + 5)^2 = 3 \)
3. \( (x - 3)^2 + (y + 5)^2 = 9 \)
4. \( (x + 3)^2 + (y - 5)^2 = 3 \)
---
**Explanation:**
To write the equation of a circle, we use the standard form:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given:
- Center \((h, k) = (-3, 5)\)
- The circle is tangent to the y-axis, meaning the distance from the center to the y-axis is equal to the radius \(r\).
The radius \(r\) will be the absolute value of the x-coordinate of the center since it is tangent to the y-axis.
So,
\[ r = |-3| = 3 \]
Thus, the equation of the circle is:
\[ (x + 3)^2 + (y - 5)^2 = 3^2 \]
\[ (x + 3)^2 + (y - 5)^2 = 9 \]
Therefore, the correct option is:
- \( (x + 3)^2 + (y - 5)^2 = 9 \)
This option corresponds to the first choice in the given list.
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