Question 22 Write the equation of the circle centered at (1, 2) that passes through (- 20, 20). Question Help: D Video Check Answer
Question 22 Write the equation of the circle centered at (1, 2) that passes through (- 20, 20). Question Help: D Video Check Answer
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Question 22**
Write the equation of the circle centered at \((1, 2)\) that passes through \((-20, 20)\).
[Text Box]
*Question Help:* [Video]
[Check Answer]
---
**Explanation:**
To solve this problem, use the formula for 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.
1. The center of the circle is \((1, 2)\), so \(h = 1\) and \(k = 2\).
2. The point \((-20, 20)\) lies on the circle, so you can use it to find the radius \(r\) by substituting into the equation:
\[
(-20 - 1)^2 + (20 - 2)^2 = r^2
\]
\[
(-21)^2 + 18^2 = r^2
\]
\[
441 + 324 = r^2
\]
\[
765 = r^2
\]
The equation of the circle is:
\[
(x - 1)^2 + (y - 2)^2 = 765
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f6caa2a-1b8e-4f41-b7cf-02fd7698df10%2F0823b690-6616-45ef-9d2e-0f2ebf0e9305%2F3w4csy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 22**
Write the equation of the circle centered at \((1, 2)\) that passes through \((-20, 20)\).
[Text Box]
*Question Help:* [Video]
[Check Answer]
---
**Explanation:**
To solve this problem, use the formula for 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.
1. The center of the circle is \((1, 2)\), so \(h = 1\) and \(k = 2\).
2. The point \((-20, 20)\) lies on the circle, so you can use it to find the radius \(r\) by substituting into the equation:
\[
(-20 - 1)^2 + (20 - 2)^2 = r^2
\]
\[
(-21)^2 + 18^2 = r^2
\]
\[
441 + 324 = r^2
\]
\[
765 = r^2
\]
The equation of the circle is:
\[
(x - 1)^2 + (y - 2)^2 = 765
\]
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