Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem: Finding the Equation of a Circle**
Find an equation of the circle in standard form with center at \( (1, 5) \) that is tangent to the x-axis.
**Equation in standard form:**
[ ]
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**Explanation:**
- The center of the circle is at the point \( (1, 5) \).
- The circle is tangent to the x-axis, meaning the distance from the center to the x-axis is equal to the radius.
- Since the center's y-coordinate is 5, the radius is 5.
**Solution:**
The standard form of a circle is \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
- Center \( (h, k) = (1, 5) \)
- Radius \( r = 5 \)
Equation: \( (x - 1)^2 + (y - 5)^2 = 25 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff07f1948-7bc7-44b0-b956-514fa1b4223b%2Fa85afe77-0e1f-4a8b-a3a9-4239826656be%2Fl71b3a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Finding the Equation of a Circle**
Find an equation of the circle in standard form with center at \( (1, 5) \) that is tangent to the x-axis.
**Equation in standard form:**
[ ]
*Submit Question Button*
**Explanation:**
- The center of the circle is at the point \( (1, 5) \).
- The circle is tangent to the x-axis, meaning the distance from the center to the x-axis is equal to the radius.
- Since the center's y-coordinate is 5, the radius is 5.
**Solution:**
The standard form of a circle is \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
- Center \( (h, k) = (1, 5) \)
- Radius \( r = 5 \)
Equation: \( (x - 1)^2 + (y - 5)^2 = 25 \)
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