Write the equation of the circle centered at (2, - 1) that passes through (14, – 13).

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°.
icon
Related questions
Question
Plz step by step
### Question 3

**Write the equation of the circle centered at (2, -1) that passes through (14, -13).**

---

**Submit your question below for help:**
[Submit Question]

or refer to the provided video tutorial for further assistance:
[Video]

--- 

### Explanation:
To find the equation of a circle in the standard form \((x - h)^2 + (y - k)^2 = r^2\), we need the center \((h, k)\) and the radius \(r\).

Given:
- The center of the circle \((h, k) = (2, -1)\)
- A point on the circle \((x_1, y_1) = (14, -13)\)

First, calculate the radius \(r\) as the distance between the center and the given point using the distance formula:
\[ r = \sqrt{(x_1 - h)^2 + (y_1 - k)^2} \]

Substitute the coordinates:
\[ r = \sqrt{(14 - 2)^2 + (-13 + 1)^2} \]
\[ r = \sqrt{12^2 + (-12)^2} \]
\[ r = \sqrt{144 + 144} \]
\[ r = \sqrt{288} \]
\[ r = 12\sqrt{2} \]

Now, substitute \(h\), \(k\), and \(r\) into the standard form equation:
\[ (x - 2)^2 + (y + 1)^2 = (12\sqrt{2})^2 \]
\[ (x - 2)^2 + (y + 1)^2 = 288 \]

Thus, the equation of the circle is:
\[ (x - 2)^2 + (y + 1)^2 = 288 \]
Transcribed Image Text:### Question 3 **Write the equation of the circle centered at (2, -1) that passes through (14, -13).** --- **Submit your question below for help:** [Submit Question] or refer to the provided video tutorial for further assistance: [Video] --- ### Explanation: To find the equation of a circle in the standard form \((x - h)^2 + (y - k)^2 = r^2\), we need the center \((h, k)\) and the radius \(r\). Given: - The center of the circle \((h, k) = (2, -1)\) - A point on the circle \((x_1, y_1) = (14, -13)\) First, calculate the radius \(r\) as the distance between the center and the given point using the distance formula: \[ r = \sqrt{(x_1 - h)^2 + (y_1 - k)^2} \] Substitute the coordinates: \[ r = \sqrt{(14 - 2)^2 + (-13 + 1)^2} \] \[ r = \sqrt{12^2 + (-12)^2} \] \[ r = \sqrt{144 + 144} \] \[ r = \sqrt{288} \] \[ r = 12\sqrt{2} \] Now, substitute \(h\), \(k\), and \(r\) into the standard form equation: \[ (x - 2)^2 + (y + 1)^2 = (12\sqrt{2})^2 \] \[ (x - 2)^2 + (y + 1)^2 = 288 \] Thus, the equation of the circle is: \[ (x - 2)^2 + (y + 1)^2 = 288 \]
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning