Write an equation of the circle with center (4, -3) and radius 8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Write an equation of the circle with center \((4, -3)\) and radius 8.
**Solution Explanation:**
To write the equation of a circle, we use the standard form of the circle's equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
**Given:**
- Center \((h, k) = (4, -3)\)
- Radius \(r = 8\)
**Substitute the values into the formula:**
\[
(x - 4)^2 + (y + 3)^2 = 8^2
\]
**Simplify using the given radius:**
\[
(x - 4)^2 + (y + 3)^2 = 64
\]
**Final Equation:**
Therefore, the equation of the circle is:
\[
(x - 4)^2 + (y + 3)^2 = 64
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F592c3157-16ae-4adf-9e37-2db2ec2ebc8f%2Fb5937a9d-f4ad-4dbd-992a-e5e6acdd58af%2Fiiehdl9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write an equation of the circle with center \((4, -3)\) and radius 8.
**Solution Explanation:**
To write the equation of a circle, we use the standard form of the circle's equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
**Given:**
- Center \((h, k) = (4, -3)\)
- Radius \(r = 8\)
**Substitute the values into the formula:**
\[
(x - 4)^2 + (y + 3)^2 = 8^2
\]
**Simplify using the given radius:**
\[
(x - 4)^2 + (y + 3)^2 = 64
\]
**Final Equation:**
Therefore, the equation of the circle is:
\[
(x - 4)^2 + (y + 3)^2 = 64
\]
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